Information Foraging

Peter Pirolli and Stuart K. Card
UIR Technical Report Funded in part by the Office of Naval Research

January 1999

This paper has been accepted for publication in Psychlogical Review. Portions of this research were funded by the Cognitive and Neural Science and Technology Division, Office of Naval Research, under contract N00014-96-C-0097.

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ABSTRACT
Information Foraging Theory is an approach to understanding how strategies and technologies for information seeking, gathering, and consumption are adapted to the flux of information in the environment. The theory assumes that people, when possible, will modify their strategies or the structure of the environment to maximize their rate of gaining valuable information. Field studies inform the theory by illustrating that people do freely structure their environments and their strategies to yield higher gains in information foraging. The theory is developed by (a) adaptation (rational) analysis of information foraging problems and (b) a detailed process model (ACT-IF). The adaptation analysis develops (a) information patch models, which deal with time allocation and information filtering and enrichment activities in environments in which information is encountered in clusters (e.g., bibliographic collections), (b) information scent models which address the identification of information value from proximal cues, and (c) information diet models which address decisions about the selection and pursuit of information items. ACT-IF is developed to instantiate these rational models and to fit the moment-by-moment behavior of people interacting with complex information technology. ACT-IF is a production system in which the information scent of bibliographic stimuli is calculated by spreading activation mechanisms. Time allocation and item selection heuristics make use of information scent to select production rules in ways that maximize information foraging activities.

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INTRODUCTION
Humans actively seek, gather, share, and consume information to a degree unapproached by other organisms. Ours might properly be characterized as a species of informavores (Dennett, 1991). Our adaptive success depends to a large extent on a vast and complex tributary of cultural tasks that engage our physical and social environments. These tasks require increasingly sophisticated information-gathering, sense-making, decision-making, and problem-solving strategies. In this paper, we are interested in understanding these information-gathering and sense-making strategies from an evolutionary ecological perspective, treating adaptations to the flux of information in the cultural environment in much the same manner as biologists study adaptations to the flux of energy in the physical environment. Here, we propose an Information Foraging Theory that is in many ways analogous to evolutionary ecological explanations of foodforaging strategies in anthropology (Smith & Winterhalder, 1992) and behavioral ecology (Stephens & Krebs, 1986). The basic hypothesis of Information Foraging Theory is that, when feasible, natural information systems evolve towards stable states that maximize gains of valuable information per unit cost (see also, Resnikoff, 1989, p. 97). Cognitive systems engaged in information foraging will exhibit such adaptive tendencies. Rational analyses of the adaptive value of information foraging tasks can guide psychological theory just as they have in other domains (Anderson, 1991; Anderson & Milson, 1989). Providing people with an independent and improved ability to access and understand available information has been a social aim for many movements at least since the Enlightenment, and it is also the aim of more mundane and practical efforts of improving modern-day productivity. Technological innovation has lead to an explosive growth of recorded information. The number of scientific journals has been growing by about a factor of 10 every 50 years since the 18th century (Price, 1963). The number of Internet hosts has been doubling about every year since 1992, and the number of pages accessible from a computer user’s desktop has increased about five orders of magnitude in the last five years. 1 Computer users world-wide now have desktop access to more than 275 million publicly accessible World Wide Web (WWW) pages, growing at the rate of

1

For purposes of rough calculation, we take a web page to be like a file and assume a user had about 1000 files in 1993 vs 275 million World-Wide Web pages in 1998. This calculation is actually conservative, since it does not take into account the very large increase in the number of Internet users during this period, the increases in CD-ROMs, and the increases in electronic mail.

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7.5 pages every second (estimated in March 1998, Bharat & Broder, 1998). Similar, if less spectacular, observations could be made for other information sources. Such growth triggers (and is triggered by) adaptations in human information technology, since human minds, although growing in number, are limited in their ability and available time to keep pace. Providing people with access to more information is not the problem. Rather, the problem is one of maximizing the allocation of human attention to information that will be useful, a point eloquently made by Simon:
What information consumes is rather obvious: it consumes the attention of its recipients. Hence a wealth of information creates a poverty of attention, and a need to allocate that attention efficiently among the overabundance of information sources that might consume it. (H.A. Simon as quoted by Hal Varian, Scientific American, Sept. 1995, p. 200).

For Information Foraging Theory, a central problem in information gathering and sensemaking is the allocation of attention. Information Foraging Theory could also provide the scientific basis from which we might engineer new innovations that enrich the information that people process. The Task Environment of Information Foraging It has been argued that most of our everyday tasks can be characterized as ill-defined problems (Reitman, 1964; 1965). Such tasks require substantial acquisition and integration of knowledge, typically from external sources (Simon, 1973), in order to better define goals, available courses of action, heuristics, and so on. Such tasks might include choosing a good graduate school, developing a financial plan for retirement, developing a successful business strategy, or writing an acceptable scientific paper. The structure of processing and the ultimate solution are, in large part, a reflection of the particular external knowledge used to structure the problem. Consequently, the value of the external information may often ultimately be measured in the improvements to the outcomes of an embedding task. The structure of the interface between people and information repositories in the external world determines the time costs, resource costs, and opportunity costs of different information foraging and sensemaking strategies. Such costs include access, recognition, and handling costs, which can be weighed against the rate at which useful information is delivered to an embedding task. Our analyses will often concentrate on developing an understanding of the amount of valuable information per unit time that is yielded by an interface between people and information repositories. Our basic

pp. a personal archive is located in conventional shelves and office furniture. 1987). 1986). and other archival information is stored or available at further distances from the office. Sandstrom (1994) has suggested that optimal foraging theory may successfully address the complex empirical phenomena that
. we would expect strategies to evolve to improve returns on foraging. 1976) shows that action items associated with ongoing tasks are most readily at hand. Independent of our own efforts. habitat choice (Cashdan. 1992). 1986). group size (Smith. Resnikoff (1989. 1976). Over time. Evolutionary-Ecological Models of Foraging We have drawn heavily upon models and techniques developed in optimal foraging theory (Stephens & Krebs. 1991. Over time. or modify the structure of the interface if it is malleable. and many other aspects of huntergatherer culture. and consequently select. 1992). We might assume that people prefer. where it has been used to explain dietary choice (Kaplan & Hill. 112-117) presents a mathematical analysis showing that the particular hierarchical structure of the common library catalog card system minimizes manual search time. we would expect information technologies to evolve to improve foraging returns. for instance in libraries. It has had an enormous impact in anthropology (Smith & Winterhalder. variations in land tenure and food sharing (Smith. given the opportunity to evolve through learning and practice. natural and artificial information systems will evolve towards stable states that maximize gains of valuable information per unit cost Structures that are so adapted may often be recognized in physical workspaces that are home to recurrent tasks. in order to maximize their rate of gaining valuable information. 1992). Faced with information foraging tasks. 1992). Soper. A cognitive strategy will be superior to another if it yields more useful information per unit cost. Research on office organization (Case. 1983. which seeks to explain adaptations of organism structure and behavior to the environmental problems and constraints of foraging for food.Information Foraging
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assumption is that people will modify their strategies. we expect that cognitive structures and strategies will also evolve to maximize information gains per unit cost. often in stacks and piles on office surfaces. Optimal foraging theory originated in attempts to address puzzling findings that arose in ethological studies of food seeking and prey selection among animals (Stephens & Krebs. In the face of selection pressures. 1981). The close coupling between the access cost of information and propensity for being used is also noted in studies of what information is read or cited (Soper. designs that improve returns on information foraging. Alternative designs for information access systems may be compared on same grounds. Malone. time allocation (Hames.

40.C. which identify how choices are to be evaluated.. In this regard.The hand is an adaptation for manipulation because it conforms in many ways to what an engineer would expect. p. 1992). noting that in biology “adaptation is demonstrated by observed conformity to a priori design specifications. We prefer the terminology of the natural selection theorist G. We would like to think that the information foraging adaptations we observe are exaptations2 of the behavioral plasticity that humans evolved for food-foraging. These will include constraints that arise out of the task structure. Currency assumptions. but it is unlikely that we will be able to obtain data relevant to tracing this evolution. of manipulative machinery. and the readable overview of these arguments by Dennett (1995). the eloquent adaptationist stance of Mayr (1983). which limit and define the relationships among decision and currency variables. and the abilities and knowledge of a user population. Constraint assumptions. and stability of that currency. 4The use of optimization models in biology has had its controversies. Adaptation analysis is a kind of engineering analysis that is to be considered a proper component of evolutionary-ecology explanations (Winterhalder & Smith. minimization.Information Foraging
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arise in the library sciences. Examples of such information foraging decisions include how much time to spend processing a collection of information or whether or not to pursue a particular type of information content. 1992.4 Optimization models in general include the following three major components: • Decision assumptions that specify the decision problem to be analyzed. Choice principles include maximization. Information foraging theory will assume information value as currency. the eye is an optical instrument because it conforms to expectations for an optical instrument. optimization models3 are a powerful tool for studying the design features of organisms and artifacts.” (Williams. italics in original). interface technology. a priori.. Our working heuristic is to try to understand the degree to which information foraging behavior is adaptive given the environmental context in which it occurs.
. Williams (1992) who uses “optimization model” rather than “optimality model” to acknowledge a focus on the optimization process and corrective tendancies rather than the attainment of global optimal states. Example of constraints include the rate at which a person can
•
•
2 3
An adaptation to one purpose that becomes adapted to another. We call this adaptation analysis. See for example the famously critical "spandrels" paper of Gould and Lewontin (1979).

1990) are not intrinsic properties of information-bearing representations (e. developmental programs. steel-bladed tool design.. Eisenberg. 1975. Designs of organs. a possible advantageous adaptation if not blocked by other forces (for example. but
. With different
parameter values it could be a knife. satisficing can often be characterized as localized optimization (e. The use of optimization models should not be taken as a hypothesis that human behavior is classically rational. “One does not treat the optimization principle as a formula to be applied blindly to any arbitrarily selected attribute of an organism. but are forfeited by engaging in the chosen activity. a screw driver. The value of information (Repo. or many other kids of tool–many. which are of two types: (1) resource costs and (2) opportunity costs (Hames. are legacies from past and natural selection can affect them in only two ways. A more successful hypothesis about humans is that they exhibit bounded rationality or make choices based on satisficing (Simon. p. 1955). 1992). 1992. It can also optimize a design’s parameters so as to maximize the fitness attainable with that design under current conditions. etc. This is what is usually meant by optimization in biology. all activities can be analyzed according to the value of the resource currency returned and costs incurred.
Organisms are never optimally designed. they describe the possibilities of a niche. Rather.Information Foraging
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navigate through an information access interface. Resource costs are the expenditures of calories. As argued above. money. The value and cost structure of information foraging is consequently defined in relation to the embedding task and this often changes dynamically over time. Also. It can adjust the numbers of mutually exclusive designs until they reach frequency-dependent equilibria. information foraging is usually a task that is embedded in the context of some other task. often with only one design that excludes alternatives. that are incurred by the chosen activity. or the value of results returned by bibliographic search technology. & Nilan. However. Optimization models do not imply that animals or information foragers will necessarily develop so as to embrace the simple global optimum. the consequences of another adaptation). Opportunity costs are the benefits that could be gained by engaging in other activities. An analogy might be the common wooden-handed. 62). Schamber. documents) but can only be assessed in relation to the embedding task environment.g. with perfect information and infinite computational resources. 1961). etc. It is normally brought in as a way of expanding our understanding from an often considerable base of knowledge” (Williams.. 1986) and the relevance of specific sources (Saracevic. hill-climbing) with resource bounds and imperfect information as included constraints (Stigler.g. In general.

1992.Information Foraging
not all. or on-line documents. the optimal information forager is one that best solves the problem of maximizing the rate of valuable information gained per unit cost. 56. or less effortful to access. is dependent on energy intake. such as books.
. This is the essence of conventional models in optimal foraging theory (Stephens & Krebs. that faces the recurrent problem of deciding what to eat. These constraints include the profitabilities of different sources. For the bird of prey. the different food-source types will have different distributions over the environment. The different information sources (or repositories) will have different profitabilities. the different kinds of sources will be distributed in the task environment in different ways. Conceptually. this means that the different habitats or prey will have different access or navigation costs. An analogous situation in information foraging theory might be an office worker or academic researcher facing the recurrent problems of finding task-relevant information. Some will be more prevalent. These constraints include the energetic profitabilities of different habitats and prey. Birds are better adapted if they have evolved strategies that better solve the problem of maximizing the amount of energy returned per amount of effort. (Williams. given the constraints of the environment in which it lives. Information flows into the environment to be represented in different types of external media. and we assume that its fitness. than others. p. given the constraints of the task environment. In addition. Conceptually. 1986). the optimal forager finds the best solution to the problem of maximizing the rate of net energy returned per effort expended. Different species of birds of prey might be compared on their ability to extract energy from the environment. Energy flows into the environment and comes to be stored in different forms. and the costs of finding and pursuing them. such as a bird of prey. The fixed-blade constraint would rule out turning it into a drill with meshing gears. manuscripts. For the bird of prey. in terms of the amount of valuable information returned per unit cost in processing the source. Furthermore. different types of habitat and prey will yield different amounts of net energy (energetic profitability) if included in the diet. and the costs of finding and accessing them. italics in original)
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Analogies Between Food Foraging and Information Foraging Imagine a predator. in terms of reproductive success. The wood-and-steel constraint would rule it out as a hand lens.

the amount of food diminishes or depletes. our imaginary bird would deplete the berries on a bush as it ate them. and faces the decision of continuing to forage in the patch or leaving to seek a new one. as the animal forages within a patch. file drawers. or in various on-line collections. Information patches could be relatively static on-line collections such as WWW sites. libraries. from one on-line collection or WWW site to another. Often the information forager has to navigate from one information patch to another—perhaps from one pile to another. The forager must expend some amount of between-patch time getting to the next food patch. the task environment of an information forager often has a “patchy” structure. office book shelves. these activities will be intertwined in observed foraging activities. the forager engages in within-patch foraging. For instance. Frequently. Problems of Enrichment vs Exploitation The traditional patch models of optimal foraging theory deal with an unmoldable environment. In such cases there will be a point at which the expected future gains from foraging within a current patch of food diminish to the point that they are less than the expected gains that could be made by leaving the patch and searching for a new one. Information relevant to a person’s information needs may reside in piles of documents. or from one search engine result to another. By analogy. We will present models addressing these activities. or temporary collections constructed by a WWW search engine in response to user queries. Quantitative formulations of patch models in optimal foraging theory determine the optimal policies for allocating time to foraging within a food patch vs searching for new patches. Once in a patch.Information Foraging Information Patches: Problems of Time Allocation to Activities
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Patch models in optimal foraging theory concern situations in which the environment of some particular animal has a “patchy” structure. These models assume that information foragers allocate their time to between-patch vs within-patch foraging activities in ways that optimize their overall rate of gaining valuable information per unit cost. Often the person is faced with decisions much like our imaginary bird: how should time be allocated among betweenpatch foraging tasks and within-patch foraging tasks? Conceptually. imagine a bird that forages for berries found in patches on berry bushes. the empirical examples analyzed in this paper exhibit two kinds of between-patch activities that we discuss next: (a) enrichment activities and (b) scentfollowing activities. Typically. The forager must optimize its selection of feasible strategies to fit the
. For instance.

One kind of environmental enrichment is to reduce the average cost of getting from one information patch to another. 1997). 1986). or should one turn to exploiting the patches? A second kind of environmental enrichment involves making information patches that yield better returns of valuable information. people often filter their readings on a topic by first generating and filtering bibliographic citations and abstracts. or access path of information sources obtained from proximal cues. one may invest time in constructing and refining keyword queries for a search engine so that it returns lists with higher proportions of potentially relevant document citations. Such enrichment activities create the trade-off problem: should one continue to enrich patches to improve future within-patch foraging or should one turn to exploiting them? Information Diet and Scent-following: Problems of Selecting and Pursuing Items to Process Information foraging often involves navigating through spaces (physical or virtual) to find high-yield patches. Such intermediate information has been referred to as “residue” by Furnas (1997). One may also enrich information patches by using filtering processes. Diet models in optimal foraging theory deal with situations in which an organism lives in an environment containing a number of potential kinds of food sources. In keeping with foraging terminology. Conceptually. imperfect information at intermediate locations is used by the forager to decide on paths through a library or an on-line text database to target information. and discussion lists now include filters. we have elsewhere called this scent (Pirolli. That is. cost. For instance.
. Information scent is the (imperfect) perception of the value. the forager can modify the environment so as to minimize the between-patch foraging costs. news. the organism faces the problem of constructing the diet that optimizes its gain of energy per unit cost. can often mold the environment to fit the available strategies. or icons representing the sources. That is. We call this process enrichment. the forager can modify the environment so as to improve within-patch foraging results. As we noted above.Information Foraging
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constraints of the environment. a species of predator may exist in
5
Foraging theorists have also dealt with the more complex problem of optimizing mixtures of nutrients (Stephens & Krebs. office workspaces tend to evolve layouts that seem to minimize the between-patch search cost for needed information. such as bibliographic citations. The information forager. however. Such enrichment activities create the trade-off problem: should one invest in reducing between-patch foraging costs. For instance. Many computer systems for electronic mail. 5 For instance. For example. WWW links.

1986). our model of scent-following is dynamic. Scent-following is very much like heuristic search studied in human problem solving and in artificial intelligence. or the text snippets found on WWW pages that represent linked documents. As the state of the forager changes through the foraging process. The profitability of an information source may be defined as the value of information gained per unit cost of processing the source. If scent is sufficiently strong. or may be more or less faster to find. These prey may have different amounts of prevalence. For example. It has been noted in biology that predators will often ignore potential low-profitability prey in order to seek out higher-profitability prey. Our notion is that the proximal perception of information scent is used to assess the profitability and prevalence of information sources. then clearly less profitable prey should be ignored if they would prevent the predator from the opportunity to pursue a more profitable prey. For instance. If there is no scent. The prey may differ in the amounts of energy they provide (perhaps because of their size). depending on the prevalences and profitabilities of prey species in their habitats. the forager will be able to make the correct choice at each decision point. the forager must make search decisions based on imperfect proximal information. and may differ in the amount of time they take to handle (e. the forager would perform a random walk. a predator that relentlessly pursued small hard-to-catch prey while large easy-to-catch prey were equally available would have a suboptimal diet.. which are static. It has also been noted that diets broaden to include more prey species.Information Foraging
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environments with several species of potential prey. These scent-based assessments inform the decisions about which items to pursue so as to maximize the information diet of the forager.g. Different sources will differ in their access costs or prevalences. in pursuing and consuming them). If profitability of prey is defined as the energy returned per unit of handling time. physical and electronic mail may come from a variety of sources that have different arrival rates and profitabilities. By analogy one may think of an information forager as an information predator whose aim it is to select information prey so as to maximize the rate of gain of information relevant to their task. and they will differ in profitability. low-profitability junk mail should be ignored if it would cost the reader the opportunity of processing more profitable mail. Clearly. Examples of these imperfect proximal cues include bibliographic citations or abstracts. either literally in
. or narrow to include less. These information prey might be relevant documents or document collections. In contrast to conventional diet models in optimal foraging theory (Stephens & Krebs. We might also expect the diet of an information forager to broaden or narrow depending on the prevalences and profitabilities of information sources.

. a short paper. A knowledge crystallization task is one in which a person gathers information for some purpose. Information foraging occurs as part of these tasks. then packages it into some form for communication or action. These field observations provide some sense of information foraging in the messy real world and motivate the analyses and models presented later. The results could be a briefing. These two extreme search regimes have different characteristic cost functions.
EXAMPLES OF INFORMATION FORAGING
We begin with descriptive analyses of information foraging "in the wild. We first present data from two field studies to illustrate the general phenomena of interest in information foraging. As examples. or even just a decision. Knowledge crystallization tasks are characterized by the use of large amounts of heterogeneous information. we develop a cognitive model.Information Foraging
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physical space or metaphorically in abstract search space. interleaved with activities for making sense of the information obtained and activities for generating some action or product. that is matched to data collected form people using a system for browsing and searching large collections of electronically stored documents. we present field studies of two knowledge crystallization tasks: (1) an individual task of writing a business intelligence newsletter and (2) a group task in which MBA students do research for a strategic business analysis report. makes sense of it. From these models. Both cases are descriptions of information-intensive work. These are then used as context for presenting optimization models adopted from theories of food-foraging strategies. we have examined information foraging as embedded in knowledge intensive work we call knowledge crystallization tasks. ill-structured problem-solving. but a relatively well-defined goal having to do with a selection and compaction of information relative to some purpose." In these examples. Both consist of the ill-structured activities required to sift through information available from a set of heterogeneous sources and develop a product that crystallizes the information into a more easily assimilated form. called ACT-IF. sampled from ongoing activities of the participants.

These analyses will be used to motivate formulations of patch foraging models. Informally (for details see. These concepts form a knowledge schema used to forage and make sense of incoming information. Information Needs Before presenting the analysis of information flow and physical layout it is worth sketching the information needs of the analyst. The analyst was asked to give the interviewer an annotated tour of all of the materials in the office. (b)
. We also collected samples of the analysts products and videotaped as much of his working materials as feasible. Pirolli & Card. The evolution of the workspace to this layout would have been one kind of enrichment activity. Later. the analyst produces newsletters that identify: (a) the players in a research and development field. Results and Discussion We present an analysis of the information flow in this analyst’s task environment in order to illustrate foraging activities that involve (a) scent-detection processes that serve to judge the potential relevance of information sources and (b) enrichment activities that successively filter information sources to improve the future rates of return of relevant information per unit cost.Information Foraging Example 1. each covering a specific topic in material science or computer science. and the newsletters are only one of an integrated set of business intelligence services. 1997). which are one kind of information patch. Business Intelligence Newsletter
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We studied the task of a professional technology analyst who. the analyst was asked questions that elicited his way of organizing the knowledge content of his job. We also present the layout of the analyst’s workspace and the arrangement of work piles. including filing systems and their organization. These newsletters go to a select set of subscribers to this premium service. We noted in the interviews and in the analysts’ information products that a set of concepts were used repeatedly. This layout appears to minimize foraging costs. making specific reference to the materials in evidence for newsletters in progress or recently completed as well as the other activities of his job. Method The analyst was interviewed in his office and described his work in detail. The interview and the analyst’s office were videotaped for later analysis. among other duties. writes a set of monthly newsletters. The concepts can be used to describe the information of relevance to the production of the analyst’s newsletters. Other analysts at the firm write similar newsletters on other topics.

dark fill indicates relevant documents. We assume that the analyst’s sensemaking and foraging activities largely proceed by recognizing instances of the categories in the materials scanned (e. marking articles (using an accompanying form) to be copied for himself.Information Foraging
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the markets for the technology. The categories were used for clustering and annotating articles within work piles. height indicates total documents. and his filing system was organized by these categories. the entry of a new player into the industry). Condensed information flow for Business Intelligence Newsletter example. The issues go to the next person on the routing slip and eventually back to the library. and white fill indicates irrelevant documents. Width indicates time investment in activities. The analyst scans the new issues. The analyst is an information forager with multiple information needs defined by this schema.000 Pages/Month (2525 Hrs/Month reading) Magazines to Scan 2800 Pages/Month (210) Hrs/Month 12 inch Project Pile 3000 Pages (255 Hrs) Marked Articles 1288 Pages/Month (97 Hrs/Month)
51 Citations 27 Citations
1 inch Writing Pile 250 Pages (19 Hrs)
Select Magazines To Scan
Scan & Mark
Library Copies Article
Dot & Sort
Write Article
Figure 1. Information Flow As mentioned above.g. the analyst will receive copies of articles routed to him by other analysts. In return. and indicators of future changes. recent developments. where the indicated articles are copied and
. The newsletters produced by the analyst were organized by these categories. industry and market trends. (c) applications of technological innovations and technology-based application opportunities.. New trade magazine issues are received by the organization’s library and physically circulated via routing slip to staff members. and (d) timing issues concerning items to watch. the analyst worked for an organization that publishes business intelligence reports. He also marks articles to be copied and sent to other analysts who would likely be interested in them. but do not receive that particular magazine.
Library 600 Magazines/Month 34.

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distributed to the appropriate analysts. The analyst’s organization receives about 600 magazines. As a way of stating this load in terms of reading time equivalents. one for each of the four newsletters or reports that he regularly authors. marking with a dot those of special interest or those that can be grouped around a theme and collecting a subpile about 1” thick to use in the next issue. Figure 1 is a simplified version of the analyst’s workflow. the analyst receives about 50 magazines/month for an estimated 500 articles (2800 pages/month). This means that when the analyst turns to working with a particular pile that the rate of processing relevant articles per unit time has been increased by prior enrichment activities. he begins to shape his report. each pile is cleaned up by filing some articles and discarding others so that it stays about constant size. if he were to read these at 200 words/min it would require around 210 hrs. such as titles or citations. When the analyst receives a pile of articles. (although it is impossible to assess this quantitatively in this case). Based on the number of articles marked at the time of our visit. he adds them to 12” high piles. we estimate that about 230 articles/month (1288 pages/month or 97 equivalent reading hrs) are marked. In general. As part of his work. that are less informative but also less costly to process than the full source document. From the interview and by estimating the sizes of the piles. it is possible to estimate the search space reduction as a consequence of these activities. people often perform enrichment activities on representations. Enrichment activities increase the proportion of relevant articles among those under consideration. The projects piles on the analysts’ desk serve as buffers holding about 3000 pages. he sorts the articles in the pile. From this subpile. People seem willing to accept some imperfection in their assessment of information value in return for lower costs of processing. Throughout much of this process the analyst judges the relevance (or scent) of articles by scanning titles and skimming. From time to time. At this point he telephones various contacts and people suggested by the articles and also uses their information for the report. rather than by fully reading them. but the 1” writing pile on which he bases a newsletter holds about 45 articles (250 pages or 19 hrs equivalent reading). Of these. Thus the scanning and culling activities appear to produce the following kinds of enrichment of within-patch foraging: • • The enrichment activities yield a total time cost reduction (in terms of potential reading time) of a factor of 12 over the 600 journals subscribed to by the group.
.

in each case.
Desk
Shelf
Desk
Active Project Piles Computer Reference Area
Figure 2. Surrounding this area is a set
. Several projects have more than one file.Information Foraging •
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The sorting of articles within piles to produce the 1” subpiles at the top of the 12” piles serves to further reduce foraging costs over and above the layout of piles discussed next. such as related books or articles that should get filed. Physical Workspace The analyst’s workspace was set up so as to allow his tasks to proceed with efficiency. On the surfaces surrounding this primary place is a secondary area of surfaces where other piles can be placed. Schematic layout of the Business Intelligence office. These open pile groups allow the analyst to switch quickly among his major tasks. We identified four such pile groups plus a small set of piles on shelves related to social activities. There is a primary workspace where the analyst sits and can work on his computer together with place for several piles or pages to be placed. there is a main pile associated with some other information. Figure 2 gives a schematic picture of the space.

Generally. reference areas. in the stacks.or topic-related information into physically localized clusters reduces the overall costs of accessing items when engaged in the relevant task.
. Within the library. several steps away from the chair is a set of filing cabinets. in general. forming a third tier of project storage. the following between-patch enrichment seems to have taken place: • The arrangement of task.). handbooks. or working on a particular topic. While team members worked in the library proper (i. This is. Example 2. Strategic Management Analysis6 Our second example involves analyses of one of two teams of MBA students who were studied while researching and writing a strategic analysis report. a necessary condition for the optimal arrangement of information over storage media with different costs. the observers recorded activities in semi-structured field notes. etc. When engaged in a particular task. such as piles.. Method MBA students in a strategic management course at a state university were asked to participate in this research as they were working on a regular assignment for the course. files. meeting rooms were set aside for the teams to work in. the office held an impressive amount of paper relative to its volume. 1980). or supplies. seem to be arranged such that those with higher frequency of access are placed in areas that have lower cost of access. and books. Overall. Our investigation followed the work of two teams made up of two and three individuals each. Each team had negotiated to congregate and meet with the observers at the university library. the participants
6This
•
work was conducted in collaboration with John van Gigch of the California State University. Each team was observed by two researchers. Clusters of task-related information. microfiche room. a fourth level of storage. and minimized costs of access. In the desk is a set of file drawers. text books.Information Foraging
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of reference materials such a directories. Sacramento.e. The results reported are from one of the teams although data from both groups are similar. the analyst can localize foraging to patches of relatively high proportions of relevant documents. Finally. The layout seems to exhibit structures that one would expect if it were evolving to maximize the rate of information foraged per unit time cost. In particular. This optimization policy is well-known in the design of virtual memory systems for computers (Denning.

printing from microfiche. The schema of information needs (for details. On average each article had a mean of 5. notes. there was an average of one annotation per 214 words read that encoded the source material into the analysis schema.). Work done in the reserved meeting rooms was video taped: group discussions were recorded as were individual think-aloud protocols when people worked solo. weaknesses. Each of the 18 articles that were eventually retrieved and processed by the students were found to have annotations corresponding to the schema. Subjects started with materials that included a description of the assignment. the pedagogical point of the exercise was to indoctrinate the students into using these schemata for just this purpose. market. Saturday morning activity was split between foraging in the library vs. textbook. Information Flow The assignment was due on a Monday. Our evidence for this schema comes from the students’ notes. Additional details are contained in Pirolli and van Gigch(1995). Library activity was divided among collecting bibliographic references. opportunities. Indeed. team members went home to read and summarize the collected materials. competition. and copying documents. These were discussed in a meeting lasting less than
. handouts. handouts.Information Foraging
18
made clear what they were doing.6 such annotations and the mean length of articles was 1190 words. meeting for discussions.). and our analysis of their protocols. Results and Discussion Information Needs As with the business analyst. and library information sheets.). copied articles. finding information sources. etc. etc. students had to gather library material and references.). In this case the schema identified the key elements of a strategic analysis. Following adjournment on Saturday. and final reports were collected by the investigators. strategies. (b) internal company environment (strengths. All printouts. and (c) strategic plans (problem definitions. Participants started work in the library on the prior Saturday. etc. So. threats. etc. materials from the strategic management course (notes. In order to carry out the assignment. see Pirolli & Card. The students had been asked to write a report containing a strategic management analysis of a familiar food and beverage company of their choosing from a list of such companies. otherwise the observers would ask for clarification. the MBA students appeared to have had a welldeveloped schema for judging the relevance of information. 1997) included many elements relating to: (a) external company environment (the industry.

We will concentrate here on the information foraging work Saturday morning. and white fill indicates irrelevant documents. A query yielded about 300 citations that were then rapidly scanned while still on the computer. We estimate that the printing took three of the 12 minutes. so the average citation was scanned and marked in 1. At the end of this
7
Matt Petrik. and the main nine topics of the report decided upon. height indicates total documents. The estimate is for the company’s General BusinessFile.3 X 10 Citations
300 Citations
51 Citations 27 Citations 18 Articl
Query DB (2 min)
Mark & Print (15 min)
Conference (70 m in)
Physically Obtain (165 min)
Figure 3.Information Foraging
19
one hour on Sunday. personal communication.
.
6 2. dark fill indicates relevant documents. The first activity in the morning was devoted to collecting citations using a commercial online bibliographic system containing an estimated 2. Width indicates time investment in activities. Information Access Company. The meeting reduced the citations to be pursued down to 27. the team went home to write parts of the report. evaluated for potential pursuit. The students then spent the next 2 hours 45 minutes gathering the materials from around the library. In the next three minutes. Following that meeting. Information from the Strategic Management Analysis example. 51 of these were marked and printed over a span of 12 minutes. the content represented by these materials was categorized into topics. the company annual report was found and printed. These citations and the company report were the focus of the first Saturday morning meeting.8 sec.3 million citations7. In about a half-hour.

The overall rate of return. 18 references were retrieved (some dropped out because they were not useful once found. It also appears that the proportion of relevant information increased among the documents under consideration (Pirolli & Card.05 items/min. Marking the items reduced this to 5. In particular. the group discussion processed . The availability of short. more than a factor of 16 overall improvement in expected reading time. Process Structure The analysis of the videotape of the Saturday morning meeting of the students reveals the processing structure they used to evaluate of the information they were gathering. Finally he found a shorter 334 line article and printed it. Information Diet Students did not choose to read documents just because there were relevant. 1997). and some could not be found). It would have taken 29. the students showed definite sensitivity to the costs of alternate methods of obtaining the information (in so far as they could anticipate them) and arranged their methods so as to minimize those costs and maximize returns of relevant information. The set of filters appeared to be ordered such that those with higher rates for processing items occurred earlier in the overall foraging process. in one four minute interval.7h to read the 300 articles received based on an assumed 200 words/min reading speed.6 items/min. It appears that the students evaluated the profitability of documents. in terms of potential value weighed against expected processing costs. less profitable articles from the information diet.
. It also seems that the earlier filters may produce less accurate judgments than later ones.1h.7h. they looked for short articles and the company report. Thus the participants retrieved a fairly large number of reference citations and passed them through a set of filters (Figure 3). Instead. In sum. He then found a 2431 line article and refused to print that as well. The early filters processed citations at the rate of 16. We can see the advantage of the method used by looking at the alternative cost of just reading the material.Information Foraging
20
task. For example.8h. they selected a diet of certain types of information. and physical retrieval and elimination processed . one team member was observed rejecting the printing of a 512 line full-text report found on-line.086 items/min.8 items/min. They acted so as to maximize information gain per unit time by using a set of filtering processes to enrich their future foraging within patches of information. group discussion to 2. more profitable articles drove out longer. and by actual retrieval to 1. taking the final set of 18 articles retrieved over the 212 min foraging period was . commenting that he was looking for short articles.

These evaluations and foraging decisions about the costs and benefits of specific items structured most of the remaining weekend activity and the structure of the final report. A goal to process the search output involved setting goals to process each of the labeled citation clusters. (b) process and structure traces can be used to identify recurring activity loops. & Newell. the students had 51 references and the company’s business plan printed on paper. and knowledge product construction. for details). In both field studies. The GOMS process operations were coded as well as the content generated (see Pirolli & van Gigch. Team members then went through the citation printout. and processes that indicate judgments of the profitability of sources. (c) schematic representations are used to judge the utility or relevance of information sources. The video tape of this session was transcribed and coded using a scheme based on GOMS (Card. Interspersed with this processing we observed opportunistic creation and refinement of goals and policies for foraging activities and the writing of the final report.” etc. and judged the relevancy of category clusters and citations within the categories to a kernel plan for the strategic management report. and characterizing and evaluating each of the citations listed under the cluster topic. and (d) information structures and flows in the environment can be analyzed to identify the costs and benefits that determine the rate-of-return on foraging activities.. Their goal was to decide which articles to retrieve and to understand how these would be used in their report. people seemingly expend considerable energies in getting as much valuable information in as little time as possible. Processing the clusters involved goals of characterizing and evaluating the relevance of cluster topics. Topic evaluations were largely based on (a) number of articles listed under a topic (more articles indicated importance of the topic. sensemaking.
.Information Foraging
21
This process structure observed in the field bears strong similarity to the processing structure we studied in the laboratory. General Discussion of the Examples The two examples illustrate that: (a) there is an interleaved set of activities devoted to foraging. and (b) relevancy to the kernel plan or the analysis outline handout.” “joint-ventures. Both cases exhibit processes or structures that enrich rates of return on foraging. 1995. Citations were often evaluated by recency of publications. At the point of this meeting. 1983). but only a sample of the articles were needed). Moran. which was organized (by the retrieval system) into subcategories such as “advertising. discussed below.

searching for the next item) and (2) within-patch (e.g. For now.g. Then. We assume that (a) the number of patches processed is linearly related to the amount of time spent in between-patch foraging activities. and (d) the average time to process patches is tW. Although the conventional models rest on strong assumptions. 1959) as the ratio of the total net amount of valuable information gained. (b) the average time between processing patches is tB. and exploiting within patches.. we apply the conventional models and the ACT-IF model to data obtained from an experiment on human information foraging. TB. TW.Information Foraging
22
CONVENTIONAL MODELS OF FORAGING
We now present some conventional models of optimal foraging and discuss their relation to the foraging activities illustrated in our field examples. we discuss a model that applies when between-patch and within-patch activities can be carried out in parallel. 1982).
λ = 1/ t B . exploiting an item). Below. G = λTB g . Likewise. we leave the notion of patch undefined: it may be a collection of documents or an individual document viewed as a collection of content. G
T +T B W
R=
information-value-units/cost units. they provide a number of basic qualitative results that appear to be broadly applicable even when the assumptions are relaxed (Stephens & Charnov. We can characterize this (Holling. the total amount of within-path time can be represented as. (3)
.) We may make some assumptions that allow us to construct a version of Equation 1 based on averages. Later. Let R be the rate of gain of valuable information per unit cost.
(1)
(The Appendix lists the definitions of variables used in models throughout this paper. (c) the average gain per item is g. G.
(2)
is the average rate of encountering patches.. This will serve as the grounds for our development of the ACT-IF cognitive model of foraging. divided by the total amount of time spent between-patches. The total amount of information gained can be represented as a linear function of between-patch foraging time as. Let us begin with a simplifying assumption that a forager's activities may be divided into two mutually exclusive sets: (1) between-patch (e.

Equation 1 may be re-written as R=
23 (4)
λTB g TB + λTBtW
λg . The patch model assumes that there may be different kinds of information patches.
π = g / tW . Time Allocation Within and Between Information Patches The conventional patch model of optimal foraging theory (Stephens & Krebs. R. Once in a patch. Using Equation 5 as context. π . Decreasing the between-patch costs. under certain strong assumptions. increasing prevalence λ ) increases the overall rate of return R towards an asymptote equal to the profitability of patches. 1986) is an elaboration of Equation 5. 2. as well as their impact on the overall rate of gaining valuable information per unit cost. which we may index using i = 1.
(6)
Increasing the profitability of within-patch activities increases the overall rate of gain. we can now state more precisely the meaning of prevalence and profitability.. . It addresses the optimal allocation of total time to between-patch activities vs within-patch activities. the
. which is under the control of the forager (this is the decision variable for the patch model). 1959). R = π .P. of patches is the ratio of net value gained per patch to the cost of within-patch processing.. t B (or equivalently. Stephens and Charnov (1982) have shown that broadly applicable stochastic assumptions lead asymptotically to Equation 5 as foraging time grows large. It serves as the basis for deriving other foraging models. = 1 + λtW
(5)
This is what’s known as Holling’s Disc Equation (Holling. The patch model assumes that the forager must expend some amount of time going from one patch to the next. The prevalence of information patches in the environment is captured by λ (the rate of encountering patches) and the profitability.Information Foraging TW = λTBtW . Rather than having a fixed average gain per patch and a fixed average within-patch cost the patch model assumes that (a) there may be different kinds of patches and (b) that the total gains from a patch depend on the within-patch foraging time.

1 + ∑ λi tWi
. For a particular type of patch. In this example. to spend within each type of patch. the function gi(tWi) in Figure 4. Likewise. Now imagine that the forager can decide to set a policy for how much time. where the relevant items occur randomly in the list. there is a linear increase in cumulative within-patch gains up to the point at which the patch is depleted.Information Foraging
24
forager faces the decision of continuing to forage in the patch or leaving to seek a new one.
i =1
P
(8)
The overall average rate of gain will be G TB + TW TB ∑ λi gi (twi )
i =1 P
R=
=
TB + TB ∑ λi twi
i =1
P
. We assume that patches of type i are encountered with a rate λi as a linear function of the total between-patch foraging time. G=
∑ λ T g (t
i B i i =1 P i =1
P
wi
) (7)
= TB ∑ λi gi (twi ).
(9)
=
∑ λ g (t
i i i =1 P i =1
P
Wi
) . represents the cumulative amount of valuable information returned as a function of within-patch foraging time tWi. the cumulative gain function increases linearly. tWi . the total amount of time spent within patches could be represented as. for an information forager who collects relevant citations from a finite list of citations returned by a search engine. This might occur. for example. As the forager processes the items. TB. TW = ∑ λi TBtwi
i =1 P
= TB ∑ λi twi . and when the end of the list is reached the patch is depleted and the gain function plateaus. The total gain could be represented as.

t2. then decrease. Such a line would be just a horizontal overlay of the x-axis. and passing through the origin gives a slope equal to the optimal average rate of gain. then there is a decrease in the overall gain rate. The slopes of these lines would at first progressively increase until they were equal to R*. such as R1. Imagine drawing a series of lines as follows. R*. imagine drawing a series of lines intersecting the gain curve at points corresponding to successively larger investments of within-path time. t2. All of this fits our intuitions. When the patch is exhausted the forager should move on the next patch. It would have zero slope. or t*. We want to emphasize the graphical reasoning used in Figure 4. To see graphically the average rate of gain R that would be achieved by different policies. at a particular within-patch time policy. Figure 4 shows three possible within-patch time allocation policies.
. from the origin and intersecting with the gain function. or the diminishing returns curves discussed in the next section: As one increases the time allocated to within-patch foraging there is. at first. one should be moving on to find another patch. this holds true for linear gain functions that plateau. and an optimal within-patch time allocation policy of t*. . This is the result of opportunity cost: Rather than continuing to spend time in a patch that is now prodicing low yields. First imagine drawing a line from the origin to the leftmost point of the gain curve. gi. t1. In general. R. up to an optimal point. tangent to gi. a line. Next. and R*. and t*. can be seen to vary with different time allocation policies. Figure 4 illustrates graphically how the average rate of gain.Information Foraging
25
Equation 9 is the patch model for information foraging—our first variant of Equation 5. we plot lines. an progressive increase in the overall gain rate. such as Figure 4. For cases such as Figure 4 (linear but finite gains). indicating zero rate of gain. R 2. since it can be used again in the next section. The slope of these lines will be the average rate of gain because the slope will correspond to the amount of value gained from patches gi(tWi) divided by the time spent in between-patch activities tBi and the time spent within patches tWi. which would correspond to zero within-patch time. such as t1. A forger should stay in such linear gain patches until the patches are exhausted (and no longer than that). complexity is added when one considers patches that yield other kinds of gain functions. As we shall discuss in the next section.

Later we discuss how such expectations are assessed in ACT-IF. presented in detail in the Appendix. deals with situations in which foraging within a patch has a decelerating cumulative gain function. It may also occur because of redundancy in such a list—because items encountered later on the list replicate information encountered earlier in the list. finite cumulative within-patch gain function (solid line). have slopes equaling the average rates of gain produced by different within-patch time (tW) allocation policies. Dashed lines. there will be diminishing returns as a function of within-patch foraging time.Information Foraging
26
Cumulative gain g(t W) R2 R1
R*
t1 tB Between-patch time tW
t*
t2
Within-patch time
Figure 4. for an information forager who collects relevant citations from a list that has been automatically ranked with elements that are more likely to be relevant at the beginning of the list. as in Figure 5. A linear. In such cases there will be a point at which the expected future within-patch gains diminish to the point that they are less than the expected gains that could be made by leaving the patch and moving to a new one. This might occur.
. such as those in Figure 5a. Charnov's (1976) Marginal Value Theorem was developed to deal with the analysis of time allocation for patches that yield diminishing returns.e. Ri. for example. Charnov’s Marginal Value Theorem Often. the marginal value of gi) is greater than the average rate of gain R for the environment. The theorem.. The theorem predicts that a forager should remain in a patch so long as the slope of gi (i.

(a) Charnov's Marginal Value Theorem states that the rate-maximizing time to spend in patch. occurs when the slope of the within-patch gain function g is equal to the average rate of gain.Information Foraging
27
Gain
R* (a) g(tW)
Between-patch time
tB Gain
t*
Within-patch time
R2 (b)
R1 g(tW)
Between-patch time
tB1
tB2
t2* t1*
Within-patch time
Between-patch enrichment
Gain R2 g2 (tW) (c) R1 g1 (tW)
Within-patch enrichment
Between-patch time
tB
t2* t1*
Within-patch time
Figure 5. which is the slope of the tangent line R. (b) the average rate of gain increases with decreases in between-patch time costs. and (c) improvements in the gain function also increase the average rate of gain.
. t*.

The point of tangency is the point at which the slope (marginal value) of gi is equal to the slope of tangent line. These included the arrangement of office layout so as to minimize costs of accessing piles of information. we noted activities that enriched future returns on foraging. see the Appendix). Figure 5c shows that as within-patch foraging gains are improved. starting at the origin and moving to the left. or (b) the rate at which patches are encountered is λ = 1/ tΒ.
. Some activities seemed aimed at reducing between-patch foraging times. and optimal within-patch time decreases from t1* to t2*. and the optimal within-patch time decreases from t1* to t2*. which is the average rate of gain R. from g1 to g2 . The slope of the tangent will be the optimal rate of gain. The prevalence of patches in the environment (assuming random distribution) can be captured by either (a) the mean between-patch search time. see the Appendix). t*. These included the filtering activities noted in both case studies. the average between-patch time tB is plotted on the horizontal axis. Figure 5a captures the basic relations for the situation in which there is just one kind of patch-gain function. the optimal average rates of gain improve from the slope of R1 to R 2. not only does within-patch enrichment improve the overall rate of gain. Figure 5b illustrates the effects of enrichment activities that reduce between-patch time costs. Effects of Between-Patch and Within-Patch Enrichment Throughout our discussion of our field studies of information foraging. To determine the optimal rate of gain R*. In Figure 5a. We may use Charnov’s Marginal Value Theorem to reason qualitatively about these enrichment activities. one draws a line tangent to the gain function gi(tW) and passing through tΒ to the left of the origin.Information Foraging
28
Figure 5 shows graphical representations of Charnov’s Marginal Value Theorem that appear in many discussions of optimal foraging theory. As between-patch time costs are reduced from tB1 to t B2 the overall rate of gain increases from the slope of R1 to the slope of R 2. Again. Figure 5c illustrates the effects of enrichment activities that improve the returns from a patch. Other activities seemed aimed on improving the gains that would eventually be made from within-patch foraging. R. the optimal gain is achieved by spending less time within a patch (when the conditions satisfying Charnov’s Marginal Value Theorem hold. The point of tangency also provides the optimal allocation to within-patch foraging time. tB. Reducing between-patch costs not only improves the overall average rate of gain. it also reduces the optimal amount of time needed to spend within patches (when the conditions satisfying Charnov’s Marginal Value Theorem hold.

the MBA students in Example 1 decided to gather company reports for the target company and short news articles. They declined to gather company reports for other companies.. yielded by such a diet would be given by another variation on Equation 5.
(10)
i Wi
8
We are purposely ambiguous in our interchangeable use of “item” and “patch. A second variant on Equation 5 is to distinguish different types of information items. one could conceivably develop diet models that treat collections as items . and the rate of encountering items of type i is λi = 1/ tBi. and let tWi be the time required to process such items. but the students’ judgments seemed to concern selecting or rejecting items based on their profitability. and other types of documents. longer news articles. and that the forager knows information concerning the profitability and prevalence of these items. and 3. however. The details and derivation of the model are presented in the Appendix.
∑λ g R= 1+ ∑λ t
i i i∈D i∈D
. 3} represents a diet consisting of items of types 1.g. 2. Thus. e.
. and to consider which items should be pursued. 2. D = {1.. Stephens and Kreb (1986) present a combined diet and patch model in which elements are simultaneously patches requiring time allocation decisions and item types requiring diet decisions.. Let D be a set representing the diet of a forager. 2. or patch models that treat documents as patches of content that require time-allocation decisions. R. Many such documents were relevant documents. The average rate of gain. The conventional diet model of optimal foraging theory provides some insights concerning the selection of items during foraging.8 The average time between processing items of type i (or average between-patch time) is tBi.Information Foraging
29
Information Diet Selection There are many instances in which a person attempting to find relevant documents in response to a query has to decide to gather and consume the most profitable information types. The model assumes that information items (or patches) can be classified by the forager into i= 1. n types. Let gi be the average gain of valuable information yielded by processing items of type i..” It may sometimes be more natural to think of things like documents as items and collections of documents as patches.

Information Foraging
30
Optimal Diet Selection Algorithm If we assume that the time costs needed to recognized the item types are effectively zero. To simplify our
•
Add item types to the diet in order of increasing rank (i. the next diet considered contains the two most profitable types. are defined as the value of the item divided by its time cost. see the Appendix). we and let the index i be ordered such that π 1 > π 2 > . The right side of the inequality concerns the profitability of the k+1st item type. > π n . and so on. presentation. D = {1. 1986). Initially.. one may imagine an iterative process that considers successive diets of the item types. tWi
(11)
In general (Stephens & Krebs. π i = g i /t W i. decreasing profitability) until the rate of gain for a diet of the top k item types is greater than profitability of the k + 1st item type. The profitabilities of each item type. At
.. computed according to Equation 10. D = {1}. 2}. D. then an optimal diet can be constructed by choosing item types in an all-or-none manner according to their profitabilities (this is known as the zero-one rule.
(12)
The left side of the inequality in Equation 12 concerns the rate of gain obtained by the diet of the k highest profitability item types. contains just the most profitable type.. π i. Conceptually. the diet. the following algorithm can be used to determine the rate-maximizing subset of the n types that should be selected: • Rank the item types by their profitability.
πi =
gi .e.
R( k ) =
∑λ g
i =1 k i =1
k
i i
1 + ∑ λi tWi
>
gk +1 = π k +1 tWk +1 .

A similar diet-narrowing effect is obtained by increasing the prevalence (λ ) of higher ranked items. So long as the gain of the diet is less than the profitability of the next item type. then the process should go on to consider the next diet D = {1.k +1}.Information Foraging
31
each stage. We assume that these items are all encountered at an equal rate of λ k = 1. the process tests the rate of gain R(k) for the current diet containing D = {1. Adding in the next item type would decrease the rate of gain for the diet. A hypothetical example of the relationship between profitability (π) and rate of gain (R) for diets including items 1.. Increases in profitability or prevalence of high-ranked items are enrichment activities that yield a narrowing of the information diet. Equation 12 is true. 2.
1
(value/time cost)
Rate of gain
.5
πk
R(k)
R*
0 1 2 3 4 5 6 7 8 9 10
Rank of item profitability (k)
Figure 6. . occurs just prior to the point where R(k) crosses under πk . Exploration of Equation 12 shows that increasing the profitability of higher-ranked items tends to change the threshold. 2. To illustrate this graphically consider Figure 6.. the iterative process terminates. R(k) ≤ π k+1. One can see that R(k) increases at first as the diet is expanded up to an optimum diet containing the top two item types..k.. R*. and then decreases as additional items are included in the diet. Figure 6 also presents R(k) calculated according to Equation 10. and one has obtained the optimal diet.. . 2.. Figure 6 presents a set of hypothetical information items having an exponential distribution of profitabilities indicated by π k . The optimum.. k} types against the profitability of the next type π k+1. Otherwise.
. yielding fewer types of items in the diet. for diets including items up to and including each item k. ..

λ i. where λi appears on the left side of the inequality but not the right side. Reading any junk mail would cost the opportunity of doing more profitable activities. for those items is less than the expected rate of gain. then that decision should be made regardless of the barrage of junk mail received. we formulate a cognitive model that is dynamic. 1990). In general. Moreover. To use an everyday information foraging analogy: if reading junk mail is categorized as a too-low profitability item (because there are better things to pursue). the models are static rather than dynamic (dependent on changing state or time). and not upon the rate at which they are encountered. • Independence of Inclusion from Encounter Rate. the information diet model states that a class of items should be ignored if the profitability. cast at a level that abstracts away from mechanisms that organisms actually use to achieve adaptive foraging strategies. of continuing search for other types of items. 1986) is that the decision to pursue a class of items is independent of its prevalence. mechanistic. one should expect a narrowing of the information diet Conventional models of optimal foraging theory—the patch model and the diet model—have generally proven to be productive and resilient in addressing food-foraging behaviors studied in the field and the lab (Stephens. A counterintuitive implication of the diet selection algorithm (Stephens & Krebs. increases in the prevalence of higher-profitability items (or equivalently increases in their encounter rates) make it optimal to be more selective. However.Information Foraging
32
Principles of Diet Selection The diet selection algorithm suggests the following: • Principle of Lost Opportunity . They are. however. To make information foraging predictions at a level of behavioral analysis typically carried out in laboratory studies. Intuitively. as the prevalence of profitable information increases. The decision to include lower-ranked items in a diet is solely dependent on their profitability. This is because the gain obtained by processing items of that lowprofitability item type is less than the lost opportunity to get higher-profitability types of items. Generally. the inclusion of a class of items is sensitive to changes in the prevalence of more profitable classes of items.
. πi . This can be seen by examination of Equation 12. The conventional models also make the strong assumption that the forager has perfect “global” information concerning the environment. R.

Figure 7 uses single-word topic labels on the clusters to represent these summaries. This model may be considered as an extensive revision of the ACT-R production system architecture (Anderson. Pedersen. Scatter/Gather scatters documents into a set of automatically induced clusters. This model. We think this model is the most stringent test of the information foraging theory. Karger. called ACT-IF. we have shown some basic predictions about information foraging. 1992) uses the clustering of documents as the basis of a browser suitable for large numbers of documents. The user may gather the documents
. The system uses an automatic clustering algorithm. to mechanistic specifications that explain how the actions are effected. To test these predictions we specify a detailed process model. Figure 7 presents a conceptual overview of how a person interacts with Scatter/Gather. (1996) in a study of a information system for very large collections of full-text documents. ACT-IF also assumes a production rule representation of cognitive skill and a set of heuristics that select productions in ways that achieve adaptive information foraging behavior. Level 1 in Figure 7 represents a set of clusters created by Scatter/Gather (only five clusters are presented in this hypothetical interaction but 10 clusters is typical in the real system).Information Foraging
33
and having access only to information currently attended to or gained from past experience. The production system model operates by heuristics that instantiate the information diet and information patch models. assumes a network representation of declarative information and a spreading activation mechanism that computes estimates of the relevance of external sources of information. called Scatter/Gather. & Tukey. Since ACT-IF is a behaving production system. Scatter/Gather summarizes the contents of the clusters in a concise way that can be presented to users.
ACT-IF: A COMPUTATIONAL COGNITIVE MODEL OF INFORMATION FORAGING
So far. we may compare traces of its behavior against those of human information foragers. We have called our model ACT-IF in recognition of its dual heritage. based on comparing the full text of documents in a collection. This moves the discussion from analyses that explain why actions are adaptive. The Scatter/Gather Browser The Scatter/Gather system (Cutting. 1993) that incorporates information foraging predictions. We present a production system model of data collected in Pirolli et al.

the user may choose one or more clusters and request that the system display the titles in those
9This
interface was developed by Marti Hearst at Xerox PARC.
. as in Level 2 of Figure 7. and request that the system repartition the subcollection into a new set of clusters. as in Figure 7. and the user decides to read them.
Level 1 Level 2
Medicine
Invasions
Sca tter
Sca tter
Law
Foreign trade
Gather
Full collection Foreign policy New subcollection Community grants
Computers
Trade
Domestic policy
Election
Figure 7. At some point. eventually bottoming out at the level of individual documents. With each successive iteration of scattering and gathering clusters. the total number of documents in the clusters becomes smaller. On command. This process may continue until a small interesting collection of documents is created.Information Foraging
34
of interesting clusters in into a new subcollection. The user may gather those clusters of interest by pointing and selecting buttons above each cluster. then automatically scatters that pooled subcollection into another set of clusters. A new screen like Figure 8 is presented to the user containing the new set of clusters.9 The document clusters are separate areas on the screen. Figure 8 presents a typical view of the Scatter/Gather interface. the system will pool the subset of documents in these clusters. A conceptual overview of the Scatter/Gather interaction process.

The clustering in Scatter/Gather depends on a measure of inter-document similarity. 1993). The Scatter/Gather document browsing interface. the system works by precomputing a cluster hierarchy. the user may bring up the full-text of a document for viewing.. In other schemes. a binary coding). sometimes also known as a normalized correlation. where each component of a vector is associated with one of the unique content words in the document collection. The similarity of two documents may then be computed by a cosine measure. the component may contain a value indicating the presence of a word in the document (i. Scatter/Gather browsing and clustering employs methods that take the same amount of time on each iteration. Internally. Conceptually. recombining precomputed components as necessary.Information Foraging
35
clusters. The method summarizes document clusters by metadocuments containing profiles of topical words central to the cluster and the most typical
. In some schemes. Karger. 1979) represents documents as vectors of equal length. a vector component may indicate the frequency or some normalized frequency of a word in the document. independent of the number of documents clustered (Cutting. By using the mouse to click on document titles. That display window contains a list of document titles.
Figure 8.e. which is the cosine of the angle between two vectors. & Pedersen. this approach (vanRijsbergen.

The evaluation functions that select production rules in ACT-IF were developed by refining the optimal foraging models discussed above. as judged by experts.833 full-text documents collected from the Wall Street Journal. This summary is called a cluster digest.Information Foraging
36
titles. The declarative memory models the information being attended to. The corpus has been extensively used by the information retrieval community.
. goal information. Overview of ACT-IF ACT-IF consists of a production memory and a declarative memory. In information foraging tasks. and its action pattern is executed during the execution phase. and it is the cluster digests that appear in boxed subareas of Figure 8 to represent each cluster. and computer articles published by Ziff-Davis. which was created for the TREC text retrieval conference (Harman. setting of goals. Actions specify updates to declarative memory. The version we used contained 742. The production memory contains production rules which are patterns of the general form Condition → Action. Department of Energy technical abstracts. These topical words and typical titles are presented to users to provide them with a summary of the documents in a cluster. Scatter/Gather was applied to the TIPSTER text collection. such as bibliographic citations. the best match is selected. We will elaborate the diet model to address how Scatter/Gather clusters are selected. we assume that people must assess the relevance or utility of information based on available cues. the Associated Press newswire. and actions to be performed in the world. 1993). the Federal Register. Standard information retrieval tasks (queries) have been defined on it together with lists of known relevant Tipster documents. We have developed an ACT-IF model of foraging tasks with a specific version of Scatter/Gather. Topical words are those that occur most frequently in a cluster. ACT-IF operates on a basic match-execute cycle. This is test corpus used to evaluate information retrieval systems. In that version. and we will elaborate the patch model to address how time is allocated to the (a) process of collecting clusters and reclustering them vs (b) displaying the document titles in clusters and scanning them for relevant ones. and information that has been recalled from long-term declarative memory. The test corpus provides us with a common standard against which to compare performance. abstracts. The retrieval tasks involve finding as many relevant documents as possible within a time limit. and typical titles are those from documents with the highest similarity to a centroid of the cluster. During the match phase. the condition part of the production rule patterns are matched against information in working memory. Those that match are then ranked by evaluation functions.

which means that declarative memory elements are created when corresponding objects “appear” on the screen in the screen state model. These networks are used to model spreading activation effects in the evaluation of information foraging productions. Each cluster summary consists of topical words and typical titles. The model-tracer then parses the participants’ actions from the log file. We assume that text summaries on the Scatter/Gather interface spread activation through the declarative memory of the user. & Lewis. which present the cluster digests. catching it just as it has evaluated and ranked the productions that match to the current goal and state of working memory. The two main types of windows of interest are (1) the Scatter/Gather windows. Following production execution.Information Foraging
37
key words. Our ACTIF model of Scatter/Gather uses spreading activation mechanisms (Anderson. These evaluation functions implement rate-optimizing information foraging heuristics. and it uses this information to maintain a model of the Scatter/Gather screen state. Model-Tracing For the Scatter/Gather study discussed below. The model-tracer runs the ACT-IF production system for one cycle at a time. 1997). the ACT-IF production system is initialized with (a) production rules for the task and (b) the spreading activation network for the individual. the ranked list of executable productions (known as the conflict set) serves as a prediction of the relative likelihood of potential user actions. 1993) as an integral part of the assessment of information scent. updates the Scatter/Gather screen
. For each simulation of each individual Scatter/Gather user. The corresponding production in the conflict set is then chosen for execution in ACT-IF. This is what we call the detection of information scent. At this point. we modeled the task structure with a common set of production rules. Corbett. and activation simultaneously spreads from the task query. The model tracer then examines the parsed log to determine the actual user action. Activation levels are used by ACT-IF evaluation functions to determine which production rules are best to execute. and (2) titles display windows which present the titles of all the documents in a cluster. and the model tracer duly updates statistics regarding the match of its predictions against the observed user actions. A model-tracing methodology (Anderson. Boyle. 1990) was used to parse the logged interactions of Scatter/Gather participants and to match these logs against ACT-IF simulations (Pirolli. the model-tracer reads the next action from the log file. titles. we also generated a spreading activation network (Anderson & Pirolli. Changes in screen state are “perceived” by the ACT-IF production system. 1984) to represent words and inter-word memory associations in participants’ declarative memory. To model-trace (match) a participant’s log file. etc.

g. ignored. The right side of the arrows are the actions of the production rules. Processing a clusters entailed looking at the clusters and processing the elements (the text summary) for the cluster.Information Foraging
38
state model. Task structure for processing cluster windows (Figure 8) as implemented by the ACT-IF production system model On the left of the arrows in Figure 10 are mnemonic names for the productions and the conditions for matching declarative memory. and ACT-IF updates its declarative memory in accordance with any “perceived” screen changes. After a cluster had been looked at.. For each Scatter/Gather window (e. Scatter/Gather Task Structure The model of the Scatter/Gather task in the evaluation study consists of 15 production rules. goals were set to process each of the clusters on the screen. The production rules implement the task structure presented in Figure 9 and they are glossed in Figure 10. Figure 8). or deselected. or the gathered clusters could be re-clustered (scattered) or displayed. Some productions are annotated with a “(2)” to indicate
.
Process Scatter/Gather window Process clusters
Cluster summaries read?
N
Process next cluster
Y
Select an unselected cluster
Deselect a selected cluster
Scatter one or more selected clusters
Display titles in one or more selected clusters
Process Scatter/Gather window
Process Titles window
Figure 9. the cluster could be selected.

NOTICE-NEW-WINDOW (2) New window on screen ATTEND-TO-WINDOW (2) Attend to window UNATTEND-TO-SCREEN (2) Goal is to process a window & different window has appeared SHIFT-ATTENTION Another window is present PROCESS-CLUSTERS Goal is to process S/G window PROCESS-NEXT-CLUSTER Goal is to process S/G window clusters & one is unprocessed LOOK-AT-NEXT-CLUSTER Goal is to process next cluster LOOK-AT-CLUSTER-ELEMENTS Goal is to look at cluster elements SELECT-RELEVANT-CLUSTER Goal is to process SG window & there is a query & there is an unselected cluster DESELECT-RELEVANT-CLUSTER Goal is to process SG window & there is a query & there is a selected cluster DO-SCATTER/GATHER Goal is to process SG window & some clusters have been selected DO-DISPLAY-TITLES Goal is to process SG window & some clusters have been selected
→ → → → → → → → → → → →
Attend to it & set goal to process it Look at window Pop the goal
Attend to that window Set goal to process clusters
Set goal to process next cluster
Look at cluster & pop the goal & set goal to process cluster elements Look at topics and typical titles & pop the goal Select the cluster
Deselect the cluster
Scatter/Gather the window
Display the titles in the window
Figure 10. (1996).Information Foraging
39
that there are actually two copies of the productions for the two different types of window. Production rules used in the ACT-IF model of the Scatter/Gather protocols obtained in Pirolli et al.
.

These assessments are used in our ACT-IF model to predict which clusters are selected and how many. and Wj is the base level activation of cluster word j. and Sji reflects the log likelihood ratios that i is relevant given that it occurs in the context of word j. In this section. Bi reflects the log prior odds so
Bi = ln( Pr(i) ψ) Pr(i )
(14)
where Pr(i) is the probability of word i occurring in the world. Pr(i ) is the probability 1 Pr(i) that the word will not occur in the world. Following the adaptationist rationale of Equation 13 in ACT-R. we interpret Equation 13 as a Bayesian prediction of the relevance of one word in the context of other words. we describe the spreading activation model of information assessment and describe how spreading activation networks can be generated from texts in the world. The spread of activation from one cognitive structure to another is determined by some network representation where interstructure links weight the rate of activation flow. Spreading activation theories are usually interpreted as predicting that more activated structures will receive more favorable processing. The activation computation was based on that of ACT-R (though not actually computed by the ACT-R architecture). The ACT-IF simulations used an evaluation function that rated cluster matching productions based on the activation of the task query when a cluster summary and its words were in the focus of attention. A i in Equation 13 is interpreted as reflecting the log posterior odds that i is relevant. Spreading Activation as a Bayesian Model of Relevance Spreading activation theories of human memory generally predict how a resource called activation is spread from cognitive structures that reside in a focus of attention.Information Foraging Assessment of Information Scent by Spreading Activation
40
Spreading activation provides the mechanism modeling people’s assessment of information scent. S ij is the association strength between cluster word j and query word i. The spreading activation networks are based on the following equations used to derive the values in Equation 13. The activation of a query word i is
Ai = Bi +
∑W S
j
j ji
(13)
where Bi is the base-level activation of i. Bi is the log prior odds of i being relevant. and ψ is a normalizing constant used to
.

Specification of Spreading Activation Networks The ACT-IF simulations of Scatter/Gather require actual spreading activation networks to compute information scent assessments. as well as the pairwise cooccurance frequencies of words that occur within 40 words of one another. To create this system. This requires statistics concerning the base rates and cooccurance statistics for the text. extracted all the text they encountered. These networks must specify the base-level activation and interassociation strengths for all the screen text encountered by an individual participant as they work with the Scatter/Gather interface. These statistics were computed from the raw text as described in Pirolli (1997). sij reflects the log likelihood ratio
s ji = ln( Pr( j | i) ψ) Pr( j | i )
(15)
where Pr(j|i) is the conditional probability of word j occurring in the context of word i and Pr( j | i ) is the conditional probability of word j occurring in a context that does not contain word i. They were calculated by making use of some intermediate results produced as a side effect of building an experimental system that automatically creates a thesaurus. and generated a spreading activation network. Moreover. Wj is the analogous value for each word j. Schuetze (1992) computed an index containing the base rate frequencies for all words in the Tipster corpus used in our Scatter/Gather study. spreading activation is also sensitive to thesaurus relations (words with different surface form but related word sense). In addition to being sensitive to raw word overlap between a query and a cluster summary. For each simulation of a participant interacting with Scatter/Gather we preprocessed their on-line log files. Anderson (1993) provides arguments for the adaptiveness of Equations 13 to 15. Pirolli (1997) performed comparisons of an earlier version of ACT-IF spreading activation against two other information retrieval methods of determining the relevance of cluster digests to queries.
. as we discuss below. spreading activation from the Scatter/Gather interface and task queries seems to be especially adept at providing proximal assessments of the whereabouts of relevant information. looked up the relevant statistics in Schuetze’s index.Information Foraging
41
yield positive values (this was set to e17 based on inspection of the raw statistics). It should be noted that the version of spreading activation embodied in Equations 13 to 15 is a mechanism that updates Bayesian a posteriori logarithmic odds based on a priori estimates and current contextual evidence.

Combining Activation from Cues When a person reads a citation.Information Foraging
42
One nagging question is how well the spreading activation network computed for each person actually reflect the person's memory structure for words. ACT-IF assumes this proximal stimulus is composed of a set of cues and spreading activation provides a model of how activation spreads from cues in the environment and features of the information goal.. The assumption might also seem justified if we knew that the amount of experience with the corpus that was observed in our studies was enough to enable the users to learn the underlying corpus statistics. We do not really know this for sure. or other pointer to an information source. 1978). Rather. For the ACT-IF model of Scatter/Gather. In the case of Scatter/Gather. multiplicative) manner. ACT-IF assumes an assessment that is like the assessment of the match of stimulus cues to stored representations in exemplar-based categorization models (Kruschke. a word) is not independent of the relevance of other cues.g. Future work will be required to test the validity of the spreading activation networks obtained from corpora such as Tipster. 1992. the assessment.g. a summary of a document. g(c. Such an assumption would seem more justified if the text corpus were known to be representative of each participants’ past experience with text. is
. the information goals are given as the task queries. it is a proximal stimulus (information scent) that provides information about some distal source of content. and the cues from the environment are the cluster summaries and document titles presented on the Scatter/Gather interface. Medin & Schaffer. provide context for one another in determining their value or relevance to an internal representation of an information goal. although the sheer size of the corpus might be expected to mean that its word statistics were more reflective of the world of text than a smaller sample. relevance or value assessment for the individual cues combines in an interactive (e. although analyses reported in Pirolli et al (1996) suggest that people are learning quite a bit about the text corpus. such as a cluster summary or document title. We now develop a model of how patterns of activation across these goal features and cues are integrated into assessments of the potential value or relevance of the distal information source. Again we do not know this for sure. s) of the cluster summary text for the cluster c presented on screen s . ACT-IF assumes that cues forming a proximal stimulus. and the stimulus also (usually) suggests a path of access to that source.. The relevance or value of each cue element (e.

Characterization of Scent in the Scatter/Gather Environment Match of Proximal Information Scent to Distal Structure of Scatter/Gather Equation 16 provides us with a characterization of information scent: a prediction of the information forager's assessment of the prospects of finding relevant information from proximal cues. For an average Scatter/Gather state s with clusters c = 1. Information scent may fail to track the underlying distribution of relevant documents for either of two reasons: (1) the model is wrong or (2) the Scatter/Gather interface provides a poor reflection of the underlying clustering structure. We call the distribution computed by the clustering algorithm the distal distribution of relevant information dD(c). We now proceed to fit these distributions for the average Scatter/Gather state. In the case of ACT-IF. i. Good fits.Information Foraging  ∑ Ai  g(c. not post-hoc from user data.
. besides the spreading activation networks. We call the perceived distribution the proximal distribution of relevant information dP(c). in the query. 2. however. that (a) T is the only parameter estimated for our simulations and (b) this estimation is done based on a priori characterizations of the information environment. given the proximal cues available. Q. we fit activation-based assessments obtained from Scatter/Gather screen states to estimates of the actual number of relevant documents in clusters. To estimate T. The information scent model in ACT-IF is completely specified a priori from the structure of the information environment. T is a scaling factor that we estimate in the next section. and Equation 16 describes how these activations are integrated into a global assessment of all the proximal cues. activation levels reflect the log likelihoods that proximal cues are relevant to an information need (the query). … 10. Equation 16 is a variant of Kruschke's (1992) model of stimulus cue assessment. we may consider two aspects: (1) how the Scatter/Gather clustering algorithm has distributed relevant documents across the clusters and (2) how a person perceives the distribution of relevant documents across clusters. We may then ask how well the two distributions match. We wanted to understand if the proximal assessment of prospects tracked the actual prospects of finding relevant information in Scatter/Gather. It should be noted that. s) = exp i ∈Q   T     
43
(16)
where the summation is over the activations of all the words. should corroborate the validity of the model and the effectiveness of the interface.

2. s). the summed activation received by query words from cluster summary texts (which is the numerator of Equation 16). Using A (c) as the numerator in Equation 16. The distribution of relevant documents across clusters on a Scatter/Gather screen. d P (c ) = g (c )
∑ g (i )
i =1
10
=
exp( A (c) / T )
(18) . s) depends on each participant’s particular queries.. d D (c) = α exp( − β (c − 1)) (17)
when the c = 1. For every screen s we ranked the clusters c = 1.63. For a particular cluster rank c we computed the average activation A (c). & Hillstrom.10 These data were calculated by an autonomous computer program that determined how many relevant documents could be found in each cluster as it traversed around the cluster hierarchy. 1980). Next.
10 11
These unpublished experiments were conducted by Marti Hearst at Xerox PARC on 29 TREC queries. A(1. s).92) by the exponential. for a cluster of rank c.. for every cluster on every screen s available across all participant log files in the Scatter/Gather study.
∑ exp( A (i) / T )
i =1
10
Equation 18 was fit by numerical methods11 to Equation 17. we computed the average information scent of relevant documents as g (c). We computed A(c. Specifically. Garbow. 47 and β = . Distribution dD(c) is presented in Figure 11. we used the Levenberg-Marquardt method as developed in the public domain MINPACK alrgorithms (More. to obtain the curve in Figure 11 and to estimate the scaling factor T. 10 clusters are ranked in decreasing order of proportion of relevant documents. can be calculated by dividing the activationassessment of a cluster by the total activation-assessments of all clusters on the same screen..
.Information Foraging
44
We made use of data from computational experiments on the Scatter/Gather clustering algorithm. s). we computed A(c. A(c. s) > A(2..12 Note that achieving the fit in Figure 11 with only one free parameter (T) is not always possible. 10 in decreasing order of activation value. s) > … > A(10. . 2. In other words.. The free parameter estimates from fitting Equation 17 to the data are α = . for a particular screen state s. . The average proportion dD(c) of relevant documents in Scatter/Gather clusters for an average query is well-fit (R 2 = .

15 . The scaling factor T is known as “temperature” in the Boltzman formula.25 . 1992).05 0 0 1 2 3 4 5 6 7 8
d P ( c) dD(c)
9
10
Rank of Cluster (c)
Figure 11. dD. Clusters are ranked in decreasing order of proportion relevant documents. Optimally.
. The distributions characterize the proportion of all the relevant documents (in an average system state) that fall in each cluster.40 .20 .
The match of dD(c ) to dP(c) in Figure 11 illustrates how well the assessment of prospects from proximal cues fits the actual distribution of relevant documents across clusters in an average Scatter/Gather state. characterizing the clustering algorithm. distal.50
Proportion of Relevant Documents
. distribution of relevant documents.Information Foraging
45
.30 . dP. characterizing information scent from the Scatter/Gather screen. The underlying.35 .10 . One may also examine what happens these prospects as a person moves from one Scatter/Gather state to another—as they iteratively gather clusters and then scatter them into a new set of clusters. and the proximal distribution. this iterative
12
Equation 18 is a Boltzman equation.45 . sometimes found in categorization research (Kruschke.

1. The basic observation is that the proportion of relevant documents across all of the clusters in state s + 1 should equal the proportion of relevant documents (relevant documents divided by total number of documents) in the clusters that were gathered in state previous state s. 2. we can write this relationship as:
∑ g(c.. First. s)
i =1
=
∑ g(i. S produced by the iterative gathering and scattering of clusters. We can ask if the proximal assessment of relevant information tracks the change in distal structure from state to state. It is another characterization of the distal structure of relevant information in the environment. . . Any task will involve a sequence of Scatter/Gather cluster states. is the total number of documents in a cluster in state s.... s)
i =1 k
k
.
.. total This is how the proportion of relevant documents changes from one state to the next as one interacts with Scatter/Gather. consider the changes in the underlying clusters as a user works with Scatter/Gather. Equation 19 says that the total proportion of relevant documents in state s + 1 is equal to the proportion of relevant documents in the k clusters gathered from state s. Each side of Equation 19 is a proportion where the numerator is the number of relevant documents assessed by activation and the denominator is the total number of documents (this value is presented on the Scatter/Gather screen). s).Information Foraging
46
process should reduce the total number of documents under consideration while increasing the proportion of relevant documents. s.. s + 1)
c =1 10 c =1
10
∑ N (c. . Letting i = 1. s + 1) ∑ N (i. relevant documents in all 10 clusters in s + 1 total relevant = documents in all k gathered clusters in s. It is a characterization of how the distal structure changes over states...
(19)
where N(c. 2. Assume that there are no backups in the process and that people iteratively gather and scatter clusters until they finally decide to display the cluster contents. k index the k gathered clusters at any state.

Information Foraging

47

Proportion Relevant Documents in all 10 clusters in next state ( s + 1)

15

10

5

0 -15 -10 -5 -5 0.00 5 10 15

-10

-15

Proportion Relevant Documents in k gathered clusters in current state s
Figure 12. Expected proportion of relevant documents in a new state (s + 1) vs the expected proportion of relevant documents in the gathered clusters from previous state s. The expected values are computed by information scent assessments by model-traces of ACT-IF. Logarithmic transformations have been performed on both dimensions. See text for details.

Figure 12 plots the Equation 19 from data obtained from our log files. We found all screen states, s, in which a person gathered clusters and then scattered them into a new screen state, s + 1. We used ACT-IF to compute the information scent provided by each cluster summary in each state using the scaling parameter T as estimated above. Figure 12 plots each one of these s to (s + 1) transitions (N = 302) as points, where the abscissa plots the model values for the right side of Equation 19 and the ordinate plots the model values for the left side of Equation 19 (both scales are logarithmic). If Equation 19 matched every transition in the log files, then all the points in Figure 12 would fall on a diagonal line though the origin. There is a good correlation (R2= .76) 13, at the predicted slope = 1, without any new parameters estimated from the data.
13

Estimated using Equation 7 of Kvålseth (1985).

Information Foraging

48

Information scent is the proximal means by which a forager judges the value or relevance of distal information sources. ACT-IF computes information scent based on spreading activation from proximal cues on the Scatter/Gather screen. Figures 11 and 12 show that the ACT-IF model of information scent tracks quite well the underlying (distal) structure of relevant information in the Scatter/Gather clustering system. Information scent matches the underlying distribution of relevant documents across clusters in the average Scatter/Gather state (Figure 11). Information scent tracks the proportion of relevant information available as one progresses from state to state in Scatter/Gather (Figure 12). The accuracy of the information scent judgements by ACT-IF corroborate the validity of the scent model and the effectiveness of the Scatter/Gather interface at communicating the underlying clusters of documents. Optimization Analysis of the Scatter/Gather Task ACT-IF uses a set of heuristics to evaluate production rules that match current conditions. These heuristics posit proximal mechanisms that generate behavior that approximate the adaptationist analysis of the conventional foraging models discussed above. These evaluation heuristics build upon the ACT-IF information scent mechanisms. To motivate the specific ACT-IF heuristics presented in the next section, we first present a more refined patch model and diet model analysis of Scatter/Gather. This refined analysis is a state space model, which is presented in the Appendix. It is based on an engineering analysis of Scatter/Gather in Pirolli (1998). The time cost parameters used in this state-space model were estimated from data collected from Scatter/Gather experts (Pirolli & Card, 1995). The analysis assumed an optimizing user that interacted as fast as possible, and who chose actions so as to maximize the overall average rate of gain, R. Characterization of Patch and Diet Problems We assume that the information patches are the Scatter/Gather display windows that contain lists of document titles. The goal of the forager is to select relevant titles from these displays. The patch (time-allocation) problem facing the information forager is the choice between (a) continuing to cluster and re-cluster documents (between-patch enrichment), or (b) beginning to display titles and forage (within-patch exploitation). The diet problem facing the information foraging is one of selecting the optimal set of clusters on each Scatter/Gather window.

Information Foraging Expected Rate of Gain for Displaying Clusters

49

During the within-patch display phase, the forager scans through a scrollable list of document titles, and must spend time processing each document citation, plus an additional amount of time processing each relevant document (i.e. cutting and pasting them into their answer file). Scanning a list of document titles should produce a withinpatch gain function such as Figure 4. As discussed above, the optimal strategy in this situation is to forage until the end of the list. The rate of return for displaying the k best clusters in a Scatter/Gather state may be characterized as No. relevant documents in gathered clusters , time between patches so far + future time within gathered clusters

RD =

The expected within-patch (i.e., within gathered clusters) time would be the time it takes to process all documents in a cluster plus the estimated additional time it would take to handle the relevant ones in the cluster (the task involves cutting and pasting relevant titles into another window), future time within gathered clusters = time on all documents in gathered clusters + time on relevant documents in gathered clusters. The Scatter/Gather interface presents the total number of documents in each cluster. For a particular cluster i, on a particular Scatter/Gather screen s, we designate the total number of documents as N(i, s). The expected time to process all documents in a set of k gathered clusters in a particular state can be characterized as the sum of the all the documents in all the gathered clusters times the estimated time it would take to process each document title, tN , t N ∑ N (i, s) .
i =1 k

Using the ACT-IF formulation of information scent in Equation 16, we can characterize the expected time it would take to process all the relevant documents in all the k gathered clusters as,

Information Foraging tg ∑ g(i, s) ,
i =1 k

50

where tg is the additional time it takes to process a relevant document title. The rate of return for displaying k gathered clusters in state s can be estimated by dividing the information scent estimate of the relevant documents in the gathered clusters by the expected time cost, which will be sum of the time spent so far tB plus the expected time within gathered clusters tW , RD ( k , s, t B ) =

In our simulations we fixed our time cost parameters to be tN = tg = 1 second/information item. Positive deviations from these values have very little effect on the results reported below. Optimal Diet of Clusters to Display To calculate the optimal collection of k clusters to display, we can evaluate R D for different collections of k clusters and choose the collection that has the maximum value of R D . According to the diet selection algorithm presented above, we may rank the clusters by their decreasing profitabilities and by considering the rates of gain produced by collections of the topmost k = 1, 2, …9 clusters. The rate-maximizing collection of clusters to display, will be,
* RD ( s, t B ) = max RD ( k , s, t B ) k =1, 2 ,...9

(21)

Expected Rate of Gain for Gathering and Re-Scattering Clusters To evaluate gathering and re-clustering clusters we assume that the information forager projects the rate of gain that would be achieved by performing one more step of clustering and then displaying the titles and foraging. The look-ahead assumes that the

i =1.
. s.Information Foraging
51
gathering and reclustering will take t ∆ additional time. The ratemaximizing collection of clusters to gather and re-scatter will be. the rate-maximizing collection of k clusters to gather and recluster is found by ranking clusters in decreasing order of profitability. The data for Figure 13 were produced by running the state space model and varying the amount of time invested in cycles of scattering and gathering clusters... 2. that the number of total documents will change by factor ∆g and the number of relevant documents will change by factor ∆N.9
(23)
Enrichment The optimizing forager invests in between-patch Scatter/Gather time in order to enrich within-patch foraging. Each cycle of gathering and re-scattering clusters is aimed at improving the proportion of relevant documents under consideration. Figure 13 shows the effect of this enrichment process. t B ) = . s) + ∆g tg ∑ g(i. Figure 13 plots the proportion of relevant documents in Scatter/Gather states that occur along a sequence of interactions with Scatter/Gather that assumed that the forager always gathered the rate-maximizing set of clusters and reclustered them. s.. …9 clusters.  k  ∆g ∑ g(i. k    k  (t B + t∆ ) + ∆N  t N ∑ N (i. s)  i =1   i =1 
(22)
Similar to Equation 21. s)  i =1  RSG ( k . and it also reduces the total number of documents under consideration. At each cycle of scattering and gathering clusters.
* RSG ( s. t ) = max RSG (i. and determining the rates of gain for collections of the topmost k = 1. the model selects the rate-optimizing set of clusters according to Equation 23. 2 . t ) .

Figure 14 was produced by running the state space model.6
. after another round of gathering and rescattering clusters. During the rising portion of the graph.2
0 0 100 200 300 400 500 600 700 800 900
Time (sec)
Figure 13. Figure 14 shows that both these rates rise at first then drop.4
. plotted as a function of time invested in scattering and gathering. and (b) RSG*. that could by achieved by one more round of scattering and gathering clusters.8
. Proportion of all documents that are relevant on Scatter/Gather windows. and always selecting the rate-maximizing collection of clusters. this means that displaying titles for the current state will not be as productive as displaying titles in the next state. To show the decision rule for this problem we present Figure 14. which displays the changing evaluations of these options over time. assuming hill-climbing heuristics.Information Foraging
52
1
Proportion Relevant Documents in Scatter/Gather state
. the maximum rate of gain. During the declining portion of the graph. displaying titles for the
. the maximum rate of gain that could be achieved by foraging through a display of titles. the simulation would determine (a) RD*.
Patch Decision Problem The patch problem for Scatter/Gather involves the decision between the options of (a) continuing to gather and re-scatter clusters vs (b) displaying clusters and foraging through the display. varying the amount of time invested in cycles of scattering and gathering clusters. During this phase. the forager should continue scattering and gathering clusters. At each cycle of scattering and gathering.

ACT-IF matches production rule conditions to
. ACT-IF Evaluation Functions ACT-IF is a production system that selects a single production rule to execute on each cycle of operation. On each cycle.05
.01
0
0
200
400
600
800
1000
Time (sec)
Figure 14. Next we discuss how the ACT-IF model evaluates productions in ways that achieve effects similar to those discussed in this analysis of the state-space model. the forager should stop scattering and gathering clusters and should display titles. .02
. As soon as this phase is detected.Information Foraging
53
current state will be more productive than displaying titles in the next state. Figure 14 suggests a greedy hill-climbing regime: If RD* ≥ RSG* then the forager should display titles and if RSG* > RD* the forager should continue scattering and gathering clusters.06
R*SG > R *D R*D > R*SG
. assuming hill-climbing heuristics.03
.04
Rate of gain
R*D R*SG
. The average rate of gain yielded by different investments in time spent scattering and gathering clusters.

π (c. s) + t N N (c. s) =
g(c. s). s) tg g(c. The ACT-IF model for Scatter/Gather has evaluation functions of production rules in Figure 10 that are based the adaptation analysis given in the previous section: • The DO-DISPLAY-TITLES production is evaluated on the basis of the rate of gain that would be achieved by displaying and foraging through k clusters that have already been gathered. s) of the cluster. The DESELECT-IRRELEVANT CLUSTER. s) is the activation-based scent assessment in Equation 16. is greater than the current rate of gain for k clusters that have already been gathered so far. s). The ACT-IF model for the Scatter/Gather task assumes that the profitability is evaluated by:
•
•
π (c. •
. In concert. s)
(24)
where g(c. Clusters will continue to be gathered so long as the evaluation of SELECTRELEVANT-CLUSTER is greater than the evaluation of DO-SCATTERGATHER or DO-DISPLAY-TITLES. however. s) is the total number of documents in a cluster. The time cost to process all the documents in a cluster is therefore the term tN N(c. matches an already selected cluster. These evaluations are computed locally. the evaluations instantiate important aspects of the adaptation analysis provided by the state-space model: • The rule evaluations select clusters when their profitability. and the additional costs of processing relevant documents is the term tg g(c. The evaluation function is RD in Equation 20. evaluates instantiations of matching rules. This solves the diet selection problem and implements the rate-maximization summarized in Equations 21 and 23. and executes the action of the highest-evaluated instantiation. The DO-SCATTER-GATHER production is evaluated on the projected rate of gain that would be produced by one more round of having the system scatter k clusters that have already been gathered. The evaluation function is R S G in Equation 22. that it matched on the current Scatter/Gather cluster display window (state s).Information Foraging
54
information in declarative memory. based only on declarative information matched by a production rule plus a time parameter. but is evaluated on the basis of the maximum of the current rate of gains estimated by RSG and RD. s). N(c. c. The SELECT-RELEVANT-CLUSTER production is evaluated on the basis of an assessment of the profitability π(c.

or will report a prime rate move by major banks. 1993).
. Method Participants Eight adults solicited through Xerox PARC or the Stanford University graduate program participated in the Scatter/Gather portion of the study as volunteers or were paid $10/hour. The evaluations work to continue gathering clusters and scattering them until the overall rate of gain shows a projected decrease. and Diehl (1996) provides data (mostly unreported) to test our information foraging predictions. Twelve topics were drawn from the first 100 query topics used in the TREC conference. Schank. such as a cut in the discount rate. Materials and Procedure Participants were asked to read the instructions for the experiment and then use the Scatter/Gather system to find articles relevant to given topics in a large and complex collection of text documents. In this study. So long as DO-SCATTER-GATHER has a higher evaluation than DO-DISPLAYTITLES. two groups of participants used Scatter/Gather under slightly different task instructions. The experiment used the 2.Information Foraging • •
55
Clusters are deselected when their profitability is less than the expected rate of gain for already gathered clusters. When the evaluation of these two rules reverses. Here we presented additional analyses that focus on information foraging analyses and fits of the ACT-IF model.
EXPERIMENT: FORAGING WITH SCATTER/GATHER
An evaluation study of Scatter/Gather performed by Pirolli.2 gigabyte TIPSTER text collection created for the TREC conference (Harman.. the model will display titles. i. in response to or in anticipation of a federal/national-level action. A typical topic description is:
A relevant document will include a prediction about the prime lending rate (national-level or major banks'). Hearst. the ACT-IF model will continue to gather and scatter clusters.e. until R*SG < R* D.

where difficulty was measured by the mean number of expert-identified relevant documents in the Tipster collection. The four topics with the fewest (expertidentified) relevant documents (M = 46) were placed in the Hard group. information retrieval experts associated with TREC have identified relevant documents in the Tipster collections for each of the topics (Harman. and the four topics about the median number of relevant documents were placed in the Medium group (M = 303 relevant documents). then choose clusters for display. as the participants’ answer to the topic query.
. and to estimate what percentage of texts in a cluster seemed relevant to the topic. In the Scatter/Gather Relevance Rating condition. using words or short phrases). This required that the participants repeatedly scatter and gather clusters using windows such as Figure 8. Each topic-block contained one easy topic. within groups. Scatter/Gather users read a topic query and then proceeded to find as many documents relevant to the query as possible. 1993). Four blocks of topics were constructed. In the Scatter/Gather Speeded condition. The activities of participants interacting with Scatter/Gather were automatically logged. The twelve topics chosen for this experiment were selected at three levels of difficulty. according to a randomized Latin square. the four topics with the most relevant documents (M = 865) were placed in the Easy group. The display window would present a list of document titles from the chosen clusters and the participants would select relevant titles from the list. and the other two blocks were used for other activities not reported here.. Each participant completed two blocks of topics using Scatter/Gather. in that order. and one hard topic. The log files contained time-stamped records of every display presented to the participants and every Scatter/Gather action performed by participants. For most of the analyses below we combine the data for the Scatter/Gather groups. and were asked to complete additional classification and relevance activities: Given worksheets. The presentation order of blocks was counterbalanced over participants. These log files provide the test data for our ACT-IF simulation.e. one medium topic. participants were given one hour per block to find articles. Scatter/Gather participants were randomly assigned to one of two study conditions: Scatter/Gather Speeded (N = 4) or Scatter/Gather with Relevance Ratings (N = 4). participants were not given a time limit.Information Foraging
56
As mentioned above. they were asked to indicate how they would classify each presented cluster (i. The titles selected by the participant would then be saved to a file.

for each cluster i at the first Scatter/Gather iteration in all query conditions.
. relevant > Hard No. tWi for the three levels of query difficulty. which predicts that a forager should select more profitable clusters over less profitable ones: The clusters in the Easy conditions contained more relevant documents than those in the Medium or Hard conditions. This corresponds to the selection of clusters at Level 1 of document clustering in Figure 7. Table 1 presents estimates relevant to the application of an information diet model to Scatter/Gather. The first Scatter/Gather interaction corresponds to the selection of clusters at the very top level of clustering in Figure 7. relevant > Medium No. This is generally consistent with the diet model. Then we estimated the time to process each cluster selected at the first Scatter/Gather iteration.63 clusters. To apply the diet selection model we estimated the subjective assessments of the cluster profitabilities. Later. we first derived gi. π i. we examined data concerning the selection of clusters for the first step of the interactive Scatter/Gather process. Participants selected more clusters for easier tasks: for Hard queries they selected M = 1. a coarse application of the diet model predicts the qualitative ordering of the query conditions with respect to the number of clusters selected (Easy > Medium > Hard). we present the more detailed ACT-IF model for selecting clusters throughout the Scatter/Gather task. the subjective estimates of the number of relevant documents in each cluster.Information Foraging Results A General Analysis of Diet Selection for Scatter/Gather
57
As a general test of the information diet model. To estimate these subjective profitabilities. This was calculated by dividing the total time to complete the query tasks by the number of clusters selected at the first iteration. for Medium queries they selected M = 1. In particular we will test the diet model prediction concerning which clusters are selected and how many. 14 For clusters selected at the first iteration of
14
We assume that participants had gained sufficient knowledge of the Scatter/Gather system for performing these estimates based on warm-up tasks done prior to experimental conditions. relevant. and reasonably approximate quantitative predictions. where difficulty corresponded to the number of expert-identified relevant documents in the collection. Participants worked on queries at three levels of difficulty. The number of expert-identified relevant documents across the Easy. These were obtained from the N = 4 participants (out of the eight participants total) who provided ratings of the percentage of relevant documents in each cluster.38 clusters. Medium. and for Easy queries they selected M = 2. As we will illustrate.25 clusters. and Hard query tasks was such that Easy No.

040 891 379 Handling time in sec (tWi) 957 994 1.28 10.08 2. 2.09 . 1996).10 highest profitability clusters in Table 1. 14. Medium queries required 994 sec per selected cluster.824 2.. Easy ≥ Medium ≥ Hard.30
Inspection of Table 1 reveals that the general qualitative prediction is that the number of clusters selected in query conditions should be such that. which is consistent with observation.890 5.400 11. Figure 15 presents the profitability estimates from Table 1.607 1. The leftmost points are labeled with the query conditions in which the clusters occurred. One can verify that drawing imaginary lines for all diets of greater than three clusters will select more Easy query clusters than Medium. drawing an imaginary line across Table 1 is like choosing the clusters whose profitabilities lie above the imaginary line.261 Estimated profitability (πI) in relevant documents per sec.64 2. To see this.i for the top 10 profitability clusters from all three query conditions.58 1. Since the rows of Table 1 are in descending rank profitability. Table 1 lists the profitability. Optimal information diet analysis for Scatter/Gather (data from Pirolli et al. and Hard queries.. R(k).62 1.Information Foraging
58
Scatter/Gather (at Level 1 of clustering): The Easy condition required 957 sec per selected cluster. in Equation 12.43 6. π i = gi/tW. We calculated the overall average rate of finding relevant document citations. recall that Equation 12 tells us that the optimal diet can be constructed by selecting the k most profitable clusters.
.9 min. Task Condition (Rank of cluster within query condition) Easy (1) Medium (1) Hard (1) Easy (2) Easy (3) Medium (2) Hard (2) Easy (4) Easy (5) Hard (3) Participants’ estimate of net relevant documents (gi) 13.670 10. The optimal diet includes the four highest profitability clusters. which is the average time between query tasks in the same query condition. 1261 sec per selected cluster.. Table 1. for diets that included the k = 1. To do this we used tBi = 91.991 1..261 957 957 994 1.46 9.526 2.93 .261 957 357 1.

Information Foraging
59
Figure 15 also presents the estimates of the overall average rate of finding relevant items R(k) for diets of increasing numbers of clusters.e. According to this application of the diet model. R. in each cluster. Analysis of the optimal information diet.25 clusters. Medium M = 1.
16
Easy
Relevant document/second
14 12 10 8
π
Medium
Optimum
Hard
Easy
6 4 2 0 0 1
R
2
3
4
5
6
7
8
9
10
Rank profitability
Figure 15. total documents) x 100%. is indicated by the hashed line. ratings of (No. These compare favorably to the observed values: Easy M = 2. and for the Medium and Hard tasks the topmost 1 cluster should be chosen.. and Hard M = 1. The predicted optimal diet of k* = 4 clusters. for the Easy tasks. The profitability (π) of clusters is ranked and added to the diet in order of decreasing profitability until the rate of gain. the topmost 2 clusters should be chosen. i. Match to Subjective Ratings Half (N = 4) of our Scatter/Gather participants provided subjective ratings of the percentage of relevant documents they expected to find in each cluster. as calculated by Equation 12. k.
.38 clusters.63 clusters. so long as the profitability of the item is greater than R. relevant documents/No.

Our ACT-IF simulation obtains g(c . We assumed a simple linear mapping from the simulation estimates onto observed ratings. N  (25)
where a and b are free parameters. a = . Observed ratings of the percentage documents in each cluster that are relevant and the ratings predicted by activation-based assessment of information scent. is assumed to provide an assessment of the quantity of relevant information in a cluster. We fit a linear regression to the geometric mean of the participants’ ratings: Rating = a + b  g(c. We extracted these values for each cluster rated by participants. N (which is displayed on the Scatter/Gather screen) should map onto these subjective ratings. Figure 16 presents the observed and predicted ratings (R2 = . s). Figure 16 illustrates that an information scent analysis. s) and N for productions that match cluster digests on the Scatter/Gather screen (Figure 8). s)  . A straightforward hypothesis is that estimates of information scent weighted by the total number of documents in a cluster.
. g(c. g(c. Information scent in ACT-IF.92. s)/N.Information Foraging
60
7 Percentage of Relevant Documents 6
Observed Rating Predicted Rating
5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Cluster Index
Figure 16.32 and b = 232).

p < . The ACT-IF production rankings are computed at each simulation cycle over all productions that match. The histogram can be interpreted as reflecting the probability that the actions at a particular rank match the observed actions. Higher ranked productions show better chances of matching user actions. Ideally. Frequency that ACT-IF productions match observed cluster-selection actions. On each cycle of each simulation of each participant. 250 200
Frequency
150 100 50 0
Rank of Cluster-Selecting Production
Figure 17.0001.Information Foraging
61
based on an analysis of the proximal cues available in the environment. There are a total of N = 858 observations in Figure 17. the ACT-IF production system ranked productions whose conditions were matched (the conflict set of productions). The histogram in Figure 17 shows the frequency with which productions at different ranks matched the observed actions.77. We investigated how the observed cluster-selecting actions of users compared to the predicted rankings of those actions in the ACT-IF simulation. The χ 2 statistic for comparing the distribution of predicted action selection against random selection was χ 2 (10) = 400. the observed action of the user should have been the highest ranked production in the conflict set of productions on the corresponding simulation cycle. can provide good predictions of the assessments that users will make of the prospects of finding relevant information Match of ACT-IF to Traces The ACT-IF model was matched to the log files from all of the Scatter/Gather participants.
More
1
2
3
4
5
6
7
8
9
10
.

s. it appears that the threshold. we determined (a) if the clusters was selected or not by the user. t).RD(k. s) .RD(k. We should expect that select(x) > unselect(x) for positive values of x (cluster profitabilities greater than expected rate of gain). x = Cluster Profitability − Expected Rate of Gain = π (c. s) − RD ( k . s. t) computed at the time the clusters are presented to users . p < . and the probability (density) of not selecting a cluster. π(c. From these observations. x = 0. Figure 18 shows that most of the profitabilities for all clusters are close to the value of RD(k.Information Foraging
62
A strong test of Information Foraging Theory concerns the selection of Scatter/Gather clusters. x = 0.
. it is clear that there are two distributions whose modes occur on opposite sides of x = 0. is significant. For all clusters seen by Scatter/Gather users. and again: x = π(c. Clusters at state s should be selected so long as their profitability.Expected Rate of Gain) as predicted by the ACT-IF simulation. These are based on N = 2929 observations. (26)
then decisions should be (a) select a cluster when x > 0 and (b) do not select a cluster when x < 0. and unselect(x) > select(x) for negative values of x (cluster profitabilities less than expected rate of gain). If we let. As predicted. We estimated the probability (density) of selecting a cluster. t ).65. It seems to occur precisely when the cluster profitability equals the expected rate of gain. In this figure.0001. Figure 18 presents these probability density functions. Despite this. We used the ACT-IF model-tracing simulation to collect the statistics relevant to these predictions regarding cluster selection. s. The shift in probability of selecting vs not selecting clusters across the threshold. unselect(x). s) . The threshold. χ2 (1) = 50. is greater than the overall rate of gain for the clusters gathered at that state RD(k. s. t). Figure 19 gives a clearer indication of the placement of the threshold. separating the decision to select vs not select clusters occurs when profitability equals rate of gain.unselect(x). s. select(x). x = 0. separates the decision to select vs not select clusters. t). we have plotted select(x) . s). and (b) the value x = (Cluster Profitability . These densities are plotted against x = π(c.

by instantiating the information diet and information patch models. Heuristics for selecting productions in ACT-IF were developed from an adaptation (rational) analysis of the Scatter/Gather task. the ACT-IF model was determined by a priori analysis of the information foraging task and the information environment. The the spreading activation model was determined by the statistics of word frequency and word cooccurance in the document corpus. These correspondences support the basic spreading activation model of information scent. The assessment of information scent from spreading activation between external cues and a goal was modeled by a form of interactive cue combination found in exemplar-based models of categorization. The threshold determining the choice of clusters varies with Scatter/Gather state and task time. A general analysis showed that the information diet model could explain the differences in the number of clusters selected for queries of different difficulties. ACT-IF also contains heuristics that implement the information diet model and information patch model. Fits of ACT-IF to traces of Scatter/Gather users suggest that this varying threshold has a good correspondence to the varying threshold of Scatter/Gather users. This required a single scaling parameter estimated from an analysis of the concordance of proximal cues on the Scatter/Gather screen to the underlying distribution of relevant documents. A cognitive model was developed in ACT-IF by using production rules to implement a task analysis of Scatter/Gather interaction and using spreading activation to compute judgements of information scent. In other. we have cast the problems of finding information in terms of coadaptation of people and their information environments.
GENERAL DISCUSSION
In this paper. We have proposed that adaptive pressures work on users of information that are analogous to ecological
. These heuristics determine which clusters will be selected and which will not be selected. The likelihood of cluster selection by users correlated with the ACT-IF rankings of clusters.Information Foraging
64
Discussion Scatter/Gather is a complex information foraging environment. This ACT-IF model yielded good fits to users' ratings of the prevalence of relevant documents in given clusters. words.

We now proceed to explore some of these models. Search Motility and Time Allocation One difference between the two field cases was that the MBA students seemed to be much more active in their search than the business intelligence professional. Relaxing these constraints or imposing new stronger constraints gives rise to a family of related models. For instance. Bell (1991). to large-scale fine-sieved drift nets. The difference is analogous to a well-known distinction in behavioral ecology between widely-foraging predators. sit-and-wait and widely-foraging foragers are two ends of a continuum. Information Foraging under Alternate Assumptions Up to this point. and handling for a number of species. and many individuals cycle between the two extremes (Bell. We have therefore explored the use of quantitative models that have been developed to explain food-foraging strategies for analyzing adaptive pressures in human informationgathering activities. Resource Maximization The maximization of rate of gains may take the form of time minimization or resource maximization.Information Foraging
65
pressures on animal food foraging or mate selection. an individual may maximize the resource accumulated or may minimize the time spent in resource accumulation (Hames. The environment moves past a sit-and-wait forager. and one may imagine similar technological effects on information foraging. That is. 1966). In all cases there is an advantage to adopting methods that confer competitive advantages measured in benefits per unit cost. For instance. Rate Maximization: Time Minimization v. The difference can become apparent when the average rate of return of the activity is made more efficient. More generally. much like the MBA students. to baited lines on small craft. human fishers may improve their foraging efficiency as they change technologies from spears. and sit-and-wait foragers. In actuality. 1991). different foraging situations and strategies will involve different allocations of time to subsidiary tasks. the information foraging models have assumed a certain set of constraints. and alternative activities that are being forfeited have a large
. 1992). pursuit. such as webbuilding spiders (Pianka. As discussed by Hames (1992): (a) a time-minimizer does not forage for more resources if efficiency is improved. much as it does for our business intelligence analyst. presents the proportion of time allocated to search. but widely-foraging organisms move through the environment. such as sharks.

R. A model developed by McNair (1983). That is. if there is a deadline involved. addresses foragers such as web-building spiders and a variant of it has been applied to information foraging systems that have multi-threaded processing capabilities (Pirolli & Card. If the MBA students chose to read newspaper articles or company reports or whole-industry reports. Now we take into account two more complications of this simple account. Information filtering systems (Belkin & Croft. typically adopt such an approach. if foraging efficiency is improved. Assuming that λ < 1. Equation 27 (multi-threaded with queued items) becomes Equation 5 (single-threaded with zero queued items). other overlapping items arrive on the queue as a Poisson ˆ ˆ process at rate λ . 1998). then the rate of gain. Assume that while the user processes one information patch. In either case.Information Foraging
66
impact but (b) a resource maximizer either spends the same amount of time. or more. we move from a pure consideration of maximizing the rate of information gain per unit time to the related problem of
. Assume that while a user forages in an information patch. Second. that allow people to perform information foraging tasks in parallel. ˆ 1 + (λ − λ )t
(27)
ˆ Note that when λ = 0 . Information Foraging with Deadlines and Uncertainty Another strong assumption made in the conventional models was that choices made by an information forager yielded certain results. some systems will retrieve items and place them on some sort of queue for processing at the users discretion. then the reading of these sources of information would yield information as predicted by the average yield of these types. Information Encounters That Overlap in Time Equation 5 assumes that between-patch and within-patch foraging activities are mutually exclusive. The analogous situation in optimal foraging theory is that of web-building spiders who can process (eat) one insect while others are “queued up” by the spiders’ web. the outcome of a particular choice is uncertain. First. that other information patches are retrieved and placed in a queue. For instance. 1992). There are many systems. the average rate of return is improved. Selecting a particular information source entails the risk that it will produce little or no information and that the time will be wasted. however. then there is a chance that sufficient information will not be foraged in time. The Appendix shows how we can elaborate Equation 5 with simple results from queuing theory. is: R=
λg(tW ) .

(2) a set of constraints. but will become more risk-prone if facing a projected shortfall in some resource. A dominant idea in the these analyses of strategy choice.Information Foraging
67
maximizing the probability that the information gatherer will have obtained sufficient information by the time of a deadline.We are all well aware that today we live awash in a sea of paper-borne
. 1994.. 1988) are: (1) a state space. For example. This aspect of information-intensive work is familiar to all involved in it and it is a part of both of our examined field examples... 1988). & Fischhoff. and deadlines is that organisms are generally risk-aversive when they can be. Dynamic optimization models of foraging (Mangel & Clark. creating the infosphere in which cultural evolution occurs. and they have been applied to the analysis of Scatter/Gather to explore the effects of hypothetical design variations on human-computer interaction (Pirolli. Adaptation of Information to People Not only do people adapt to core complex information environments. 1988) have also addressed foraging with risk and deadlines. Katz & Rosen. The pervasiveness of similar trade-offs in human endeavors (e. Optimization techniques like dynamic programming can be used to understand the optimal foraging strategies in such systems. Ch. 1988). The analysis of strategy choice under risk and uncertainty is a large topic unto itself in disciplines such as economics (e. risk. Dennett has aptly characterized the situation. One model for risk and deadline-pressure foraging is the Extreme Variance Rule developed by Stephens and Charnov (1982). Speaking and hearing. 1976):
Human language.. sports) suggests the we should find them also in information foraging. writing and reading–these are the underlying technologies of transmission and replication most analogous to the technologies of DNA and RNA in the biosphere. using the notion of cultural knowledge units called memes (Dawkins. The essential components of such models (Mangel & Clark. but the environments of information to which people adapt are themselves complex and dynamic. written.g.g. is surely the principal medium of cultural transmission. economic behavior. and (5) a specification of state dynamics. 1998). (4) an optimization criterion. very recently. first spoken and then. (3) a strategy set. impending starvation often leads to higher risk strategies. 6) as well as psychology (Slovic. Dynamical Models of Information Foraging Dynamic optimization techniques have been used in optimal foraging theory (Mangel & Clark. Some analyses have been developed in optimal foraging theory. Lichtenstein.

The motivating analogy is the eye. 1992). 1992). Evolutionary psychology (Barkow. Related Theories There are several other approaches to cognitive psychology that are strongly motivated by ecological and evolutionary concerns. function-specific. 1992) argues for cognitive universals in mental architecture that have evolved as adaptations over evolutionary time. Cosmides. Rational analysis (Anderson. breathing in an atmosphere of electronically-borne memes. but instead focuses on general mechanisms that solve general information-processing problems posed by the environment. 1991) are characterized as adaptive solutions to recognizing naturally occurring phenotypes in the biological world. p. 1992) and certainly language (Pinker & Bloom. Analyses presented in Pitkow and Pirolli (1997) shows by survival analysis techniques that WWW page survival rates (until deletion) are correlated with the amount of visits they receive and the kind of visitors. It is argued that these information-processing problems are universal
. in addition to humans consuming information for their survival. & Tooby. for the most part. the mechanisms of memory (Anderson & Milson. Information Foraging Theory is different from and. complex arrangement of tissue that has evolved due to strong selection pressures (Tooby & Cosmides. with an emphasis on specific complexes for such activities as social exchange (Cosmides & Tooby. complementary to these other approaches. For instance. and are proving to be virtually unquarantinable. 1992). rather than unprogrammed universal computational architecture. Evolutionary psychology seeks to explain complex cognitive modules. 1990) does not necessarily deny the existence of function-specific complexes in the cognitive architecture. there is a complementary notion of information consuming humans for its survival. typically by looking back at the physical and social environments that shaped human evolution during the Pleistocene (Tooby & Cosmides. and mechanisms of categorization (Anderson. In contrast to other approaches. They leap promiscuously from vehicle to vehicle. Memes now spread around the world at the speed of light. an exquisite.
68
This analysis suggests that.Information Foraging
memes. 1995). 347. 1991). and from medium to medium. and replicate at rates that make even fruit flies and yeast cells look glacial in comparison. (Dennett. Information Foraging Theory emphasizes universals governing adaptation at the level of the modern-day task environments. 1989) are characterized as adaptive solutions to the recurrent structure of events in the world (Anderson & Schooler.

Information Foraging Theory focuses on understanding adaptation to current environments. As we stated in the introduction. To understand information foraging behavior. modern-day information foraging mechanisms may be exaptations of food foraging mechanisms that evolved in our ancestors. is to explain and predict adaptive solutions: how people will best shape themselves to the environment and how the environment can best be shaped to people. then. but it would be difficult to trace this connection. The problems and constraints of such environments can be thought of as forming abstract landscapes of information value and costs. and interpreting information-bearing documents. Information Foraging Theory frames the rational analysis of adaptations at the level of tasks rather than at the level of cognitive architecture.
. it pursues explanations that take environmental structure and variation as an essential element in the explanation of the observed behavioral structure and variation. often technologybased environments in which they perform tasks that require processing external information-bearing resources. Unlike rational analysis at the level of the cognitive architecture.Information Foraging
69
(at least at the space-time scale of terrestrial evolution) and would operate as strong selection forces to drive the evolution of general information-processing solutions at the level of cognitive architecture. and to understand the dynamics of the environment of information sources. Unlike evolutionary psychology. rendering. That is. The task of Information Foraging Theory. to analyze and design information access and visualization technologies. however. dynamic. such as the costs of accessing. Information Foraging Theory frames the analysis of complex ensembles of cognitive mechanisms and knowledge that are shaped by information foraging environments. Information Foraging Theory adopts an evolutionary ecology approach. The basic working heuristic of Information Foraging Theory is to assume that people adapt to the constraints and problems they face in complex.

Correspondence should be directed to Peter Pirolli (pirolli@parc. Xerox PARC.Information Foraging
77
AUTHOR NOTES
This research has been supported by an Office of Naval Research Grant. Palo Alto.
.com). No. Anderson and Judith Olson for their extensive constructive comments on earlier drafts. N0001496-0097. CA 94304. 3333 Coyote Hill Road. We would like to thank John R.xerox.

Inspection of Equation A. π i. Note that this occurs under the constraint that the time it takes to recognize an item is assumed to be zero.10)
The decision to set pi = 1 or pi = 0 is reduced to the following rules which determine the numerator of Equation A. and encounter rate for an encountered prey. 2.7 as being applicable when an organism can predict (recognize) the net gain.7. This provides the basis for the diet optimization algorithm presented in the main text.9 shows that R is maximized by either pi = 1 or pi = 0 (Stephens & Krebs.7 might be applied under the assumption that the modeled organism partitions the space of the observed feature combinations exhibited by its potential prey into discrete categories.9: set pi = 0 if gi/tWi < ki/ci set pi = 1 if gi/tWi > ki/ci else) For the n item types. processing time.8 obtains
∂R λ i gi ci − λ i tWi ki = .8)
where ki is the sum of all terms not involving pi in the numerator of Equation A. This is known as the Zero-One Rule which simply states that the optimal diet will be one in which items of a given profitability level are chosen all-or-none. 1986). is defined as
πi =
gi . (the profitability for i is less than for everything else) (the profitability for i is greater than for everything
. where profitability. Equation A. ci is the sum of all terms in the denominator not involving pi. In the case of food foraging. and encounter rate variables are not dependent on pi. n. there are n such inequalities. .. and we assume that the gain. processing time. ci + pi λi tWi (A..9)
Zero-One Rule. Differentiating Equation A. One may also think of Equation A. ∂pi (ci + pi λ i tWi ) 2
(A. tWi
(A. i = 1. To maximize with respect to any given pi we differentiate R= pi λi gi + ki .Information Foraging
80
probability that items of type i should be pursued (the decision variable to be set by the optimization analysis).

Information Foraging State Space Model of Scatter/Gather
81
The interaction of users with the Scatter/Gather system can be represented in a state-time space. where a state variable X<k> takes on values X<k> = x. To produce the simulation summarized in Figures 13 and 14 we set the initial state such that. such that. G(X<k>) is the number of relevant documents in all clusters in the subcollection at state X<k>. C * . and X <0> is the initial state. G(X<0>) = 303 relevant documents.12)
G(X ) =
<k>
∑ g(c. is chosen such that it maximizes RSG* as specified in Equations 22 and 23. X
c =1
C*
< k −1>
). . g(c.. X<k>) be the number of relevant documents in cluster c in state X <k> and N(c. We let g(c.k. We assume that the distribution of relevant documents across clusters is specified by Equation 17. X < k > ) g(c + 1.833 total documents.. NT(X<0>) = 742.. X < k > ) The optimal set of clusters.
(A. > N (c. NT(X ) =
<k>
(A. The state X<k> is the state at step k of the Scatter/Gather process.13)
.
(A. We use the convention that c is indexed in order of decreasing profitability. The state space is evolved for some number of steps s = 1. X < k > ) . . The state has the following components: tB(X<k>) is time taken so far on a query task. X < k > ) N (c + 1.. tB(X<0>) = 0 seconds. X
c =1
C*
< k −1>
). X<k>) is the number of total documents in cluster c in state X <k>. 2. K. and T(X<k>) is the total number of documents in all clusters in the subcollection at state X<k>.11)
∑ N (c. tB(X<k>) = tB(X<k-1>) + t∆.

Assuming the strong but simple case in which items arrive locally as Poisson events. the average length of a queue for our simple case would be
λtW .15)
items. where λ is the rate of encounter with patches and t W . a forager may expect to encounter 1+ ˆ 1 λtW = . dt where g ′(t W ) = g(tW ) . 1961). is the average time to process a patch. the revised rate of long-term gain becomes
R=
λtW 1+ ˆ 1 − λt
λg(tW ) ˆ 1 − λt
W W
=
λg(tW ) . Assuming that λ < 1.17)
15
This section elaborates the overlapping encounters patch model of Stephens and Krebs (1986). (1 − λtW )
Including the item currently handled. ˆ ˆ (1 − λtW ) (1 − λtW )
(A. 1 +t ˆ W λ −λ (A.14)
(A.16)
which is maximized under the first-order condition dR = 0.Information Foraging Patch Model with Queuing15
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A foraging model appropriate for overlapping encounters can be developed by elaborating the patch model with simple results from queuing theory (Cox & Smith. where is the rate at which overlapping items arrive during the handling of the ˆ current item.
. λtW. From queuing theory. then the average length of a queue of such encounter events is determined by traffic intensity. ˆ 1 + (λ − λtW )
(A.

Total time spent in within-patch foraging. Distribution obtained from information scent analysis of Scatter/Gather displays: the proportion of all relevant documents in a Scatter/Gather state that are allocated to cluster of rank c. when ranked by those proportions. Average information value gained per item Average information value gained per item of type i. Average activation received by clusters of rank c. Cumulative value gained in information patches as a function of time tW Cumulative value gained in information patches of type i as a function of time tWi Average time cost for between-patch foraging Average time cost for within-patch foraging Average rate of encountering information patches Time spent between patches of type i Time spent foraging within patches of type i Average rate of encountering information patches of type i Profitability of item type i Overlapping encounter rate (arrival of new items while an item is being processed) Probability of pursuing items of type i (diet decision model)
λ
tBi tWi
λι πi
ˆ λ
pi
Information Scent and Spreading Activation Models Ai Bi Sji g(c. Total information value gained.
dP (c)
A (c )
. s) T Total activation of cognitive element i Base-level activation of cognitive element i Association strength from element j to element i Activation-based estimate of expected No. relevant documents in cluster c in Scatter/Gather state s Scaling factor (Boltzman temperature)
Scatter/Gather Analyses dD(c) Distribution obtained from computational experiments on the clustering algorithm: the proportion of all relevant documents in a Scatter/Gather state that are allocated to cluster of rank c.Information Foraging
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Table A. Total time spent in between-patch foraging.1 Notation Using in the Foraging Models
Conventional Information Foraging Models R G TB TW g gi g(tW) gi (tWi) tB tW Rate of gain of information value per unit time cost. when ranked by those proportions.

Information Foraging
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g (c )
Average information scent received by clusters of rank c. No.
N T(X<k>) tB (X <k>)
N(c.
)
Number of relevant documents in a Scatter/Gather state Total number of relevant documents in a Scatter/Gather state Time spent getting to a Scatter/Gather state. Total number of documents in cluster c in state X<k>. s. X<k>)
g (c. of total documents in cluster c in Scatter/Gather state s Expected rate of gain if k gathered Scatter/Gather clusters in state s at task time tB are displayed and judged for relevance. Expected rate of gain if k gathered Scatter/Gather clusters in state s at task time tB are re-clustered Profitability of cluster c in Scatter/Gather state s Time it will take to perform a re-clustering Local rate of change in number of relevant documents and total number of documents if a reclustering is performed.
N(c. tB )
π(c. s)
∆t ∆g. ∆N
Scatter/Gather State Space Model X<k> G(X
<k>
Scatter/Gather state k. s. tB ) RSG(k. s) RD(k. Number of relevant documents in cluster c in state X<k>. X <k>)
.